Search.setIndex({"docnames": ["api/gpflow/base/index", "api/gpflow/conditionals/index", "api/gpflow/conditionals/util/index", "api/gpflow/config/index", "api/gpflow/covariances/index", "api/gpflow/expectations/index", "api/gpflow/expectations/quadratures/index", "api/gpflow/experimental/index", "api/gpflow/experimental/utils/index", "api/gpflow/functions/index", "api/gpflow/index", "api/gpflow/inducing_variables/index", "api/gpflow/inducing_variables/inducing_variables/index", "api/gpflow/kernels/base/index", "api/gpflow/kernels/index", "api/gpflow/kullback_leiblers/index", "api/gpflow/likelihoods/index", "api/gpflow/likelihoods/utils/index", "api/gpflow/logdensities/index", "api/gpflow/models/cglb/index", "api/gpflow/models/gpr/index", "api/gpflow/models/index", "api/gpflow/models/sgpr/index", "api/gpflow/models/svgp/index", "api/gpflow/models/util/index", "api/gpflow/models/vgp/index", "api/gpflow/monitor/index", "api/gpflow/optimizers/index", "api/gpflow/optimizers/natgrad/index", "api/gpflow/posteriors/index", "api/gpflow/probability_distributions/index", "api/gpflow/quadrature/gauss_hermite/index", "api/gpflow/quadrature/index", "api/gpflow/type_flags/index", "api/gpflow/utilities/index", "api/gpflow/utilities/ops/index", "api/gpflow/utilities/parameter_or_function/index", "benchmarks", "bibliography", "getting_started", "index", "installation", "notebooks/advanced/GPLVM", "notebooks/advanced/changepoints", "notebooks/advanced/convolutional", "notebooks/advanced/coregionalisation", "notebooks/advanced/fast_predictions", "notebooks/advanced/gps_for_big_data", "notebooks/advanced/heteroskedastic", "notebooks/advanced/mcmc", "notebooks/advanced/multiclass_classification", "notebooks/advanced/multioutput", "notebooks/advanced/natural_gradients", "notebooks/advanced/ordinal_regression", "notebooks/advanced/variational_fourier_features", "notebooks/advanced/varying_noise", "notebooks/getting_started/basic_usage", "notebooks/getting_started/classification_and_other_data_distributions", "notebooks/getting_started/kernels", "notebooks/getting_started/large_data", "notebooks/getting_started/mean_functions", "notebooks/getting_started/monitoring", "notebooks/getting_started/parameters_and_their_optimisation", "notebooks/getting_started/saving_and_loading", "notebooks/tailor/external-mean-function", "notebooks/tailor/gp_nn", "notebooks/tailor/kernel_design", "notebooks/tailor/mixture_density_network", "notebooks/theory/FITCvsVFE", "notebooks/theory/SGPR_notes", "notebooks/theory/Sanity_check", "notebooks/theory/cglb", "notebooks/theory/upper_bound", "notebooks/theory/vgp_notes", "user_guide"], "filenames": ["api/gpflow/base/index.rst", "api/gpflow/conditionals/index.rst", "api/gpflow/conditionals/util/index.rst", "api/gpflow/config/index.rst", "api/gpflow/covariances/index.rst", "api/gpflow/expectations/index.rst", "api/gpflow/expectations/quadratures/index.rst", "api/gpflow/experimental/index.rst", "api/gpflow/experimental/utils/index.rst", "api/gpflow/functions/index.rst", "api/gpflow/index.rst", "api/gpflow/inducing_variables/index.rst", "api/gpflow/inducing_variables/inducing_variables/index.rst", "api/gpflow/kernels/base/index.rst", "api/gpflow/kernels/index.rst", "api/gpflow/kullback_leiblers/index.rst", "api/gpflow/likelihoods/index.rst", "api/gpflow/likelihoods/utils/index.rst", "api/gpflow/logdensities/index.rst", "api/gpflow/models/cglb/index.rst", "api/gpflow/models/gpr/index.rst", "api/gpflow/models/index.rst", "api/gpflow/models/sgpr/index.rst", "api/gpflow/models/svgp/index.rst", "api/gpflow/models/util/index.rst", "api/gpflow/models/vgp/index.rst", "api/gpflow/monitor/index.rst", "api/gpflow/optimizers/index.rst", "api/gpflow/optimizers/natgrad/index.rst", "api/gpflow/posteriors/index.rst", "api/gpflow/probability_distributions/index.rst", "api/gpflow/quadrature/gauss_hermite/index.rst", "api/gpflow/quadrature/index.rst", "api/gpflow/type_flags/index.rst", "api/gpflow/utilities/index.rst", "api/gpflow/utilities/ops/index.rst", "api/gpflow/utilities/parameter_or_function/index.rst", "benchmarks.rst", "bibliography.rst", "getting_started.rst", "index.rst", "installation.rst", "notebooks/advanced/GPLVM.ipynb", "notebooks/advanced/changepoints.ipynb", "notebooks/advanced/convolutional.ipynb", "notebooks/advanced/coregionalisation.ipynb", "notebooks/advanced/fast_predictions.ipynb", "notebooks/advanced/gps_for_big_data.ipynb", "notebooks/advanced/heteroskedastic.ipynb", "notebooks/advanced/mcmc.ipynb", "notebooks/advanced/multiclass_classification.ipynb", "notebooks/advanced/multioutput.ipynb", "notebooks/advanced/natural_gradients.ipynb", "notebooks/advanced/ordinal_regression.ipynb", "notebooks/advanced/variational_fourier_features.ipynb", "notebooks/advanced/varying_noise.ipynb", "notebooks/getting_started/basic_usage.ipynb", "notebooks/getting_started/classification_and_other_data_distributions.ipynb", "notebooks/getting_started/kernels.ipynb", "notebooks/getting_started/large_data.ipynb", "notebooks/getting_started/mean_functions.ipynb", "notebooks/getting_started/monitoring.ipynb", "notebooks/getting_started/parameters_and_their_optimisation.ipynb", "notebooks/getting_started/saving_and_loading.ipynb", "notebooks/tailor/external-mean-function.ipynb", "notebooks/tailor/gp_nn.ipynb", "notebooks/tailor/kernel_design.ipynb", "notebooks/tailor/mixture_density_network.ipynb", "notebooks/theory/FITCvsVFE.ipynb", "notebooks/theory/SGPR_notes.ipynb", "notebooks/theory/Sanity_check.ipynb", "notebooks/theory/cglb.ipynb", "notebooks/theory/upper_bound.ipynb", "notebooks/theory/vgp_notes.ipynb", "user_guide.rst"], "titles": ["gpflow.base", "gpflow.conditionals", "gpflow.conditionals.util", "gpflow.config", "gpflow.covariances", "gpflow.expectations", "gpflow.expectations.quadratures", "gpflow.experimental", "gpflow.experimental.utils", "gpflow.functions", "gpflow", "gpflow.inducing_variables", "gpflow.inducing_variables.inducing_variables", "gpflow.kernels.base", "gpflow.kernels", "gpflow.kullback_leiblers", "gpflow.likelihoods", "gpflow.likelihoods.utils", "gpflow.logdensities", "gpflow.models.cglb", "gpflow.models.gpr", "gpflow.models", "gpflow.models.sgpr", "gpflow.models.svgp", "gpflow.models.util", "gpflow.models.vgp", "gpflow.monitor", "gpflow.optimizers", "gpflow.optimizers.natgrad", "gpflow.posteriors", "gpflow.probability_distributions", "gpflow.quadrature.gauss_hermite", "gpflow.quadrature", "gpflow.type_flags", "gpflow.utilities", "gpflow.utilities.ops", "gpflow.utilities.parameter_or_function", "Benchmarks", "Bibliography", "Getting Started", "GPflow", "Installation", "Bayesian Gaussian process latent variable model (Bayesian GPLVM)", "Change points", "Convolutional Gaussian Processes", "A simple demonstration of coregionalization", "Faster predictions by caching", "Stochastic Variational Inference for scalability with SVGP", "Heteroskedastic Likelihood and Multi-Latent GP", "MCMC (Markov Chain Monte Carlo)", "Multiclass classification", "Multi-output Gaussian processes in GPflow", "Natural gradients", "Ordinal regression", "Variational Fourier Features in the GPflow framework", "Gaussian process regression with varying output noise", "Basic Usage with GPR", "Classification, other data distributions, VGP and SVGP", "Kernels", "Large Data with SGPR", "Mean Functions", "Monitoring", "Parameters and Their Optimisation", "Saving and Loading Models", "Custom mean functions: metalearning with GPs", "Mixing TensorFlow models with GPflow", "Kernel Design", "Mixture Density Networks in GPflow", "Comparing FITC approximation to VFE approximation", "Derivation of SGPR equations", "Sanity checking when model behaviours should overlap", "Conjugate Gradient Lower Bound", "Discussion of the GP marginal likelihood upper bound", "Derivation of VGP equations", "User Guide"], "terms": {"valu": [0, 1, 2, 3, 9, 10, 14, 16, 19, 20, 21, 22, 23, 25, 26, 27, 29, 32, 34, 35, 36, 40, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 64, 66, 67, 68, 69, 71, 72], "sourc": [0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 40, 56], "enum": [0, 29], "an": [0, 1, 2, 3, 5, 8, 9, 10, 14, 16, 20, 21, 22, 23, 24, 25, 27, 34, 38, 40, 42, 43, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 69, 72, 73, 74], "enumer": [0, 44, 49, 64, 67], "util": [1, 3, 7, 10, 16, 21, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 59, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 74], "kmn": [1, 2], "kmm": [1, 2], "knn": [1, 2], "f": [1, 2, 9, 14, 16, 20, 21, 23, 25, 31, 32, 34, 38, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 57, 58, 59, 60, 63, 64, 66, 67, 69, 70, 72], "full_cov": [1, 2, 20, 21, 22, 23, 25, 29, 54, 56, 57, 58, 59, 60, 61, 62, 63], "fals": [1, 2, 10, 14, 15, 20, 21, 22, 23, 25, 27, 29, 32, 34, 44, 47, 48, 49, 50, 52, 53, 54, 56, 57, 58, 59, 60, 62, 63, 64, 70, 71, 72], "q_sqrt": [1, 2, 15, 21, 23, 27, 29, 44, 48, 50, 51, 52, 54, 57], "none": [1, 2, 3, 5, 6, 9, 10, 11, 12, 13, 14, 15, 16, 20, 21, 22, 23, 25, 26, 27, 29, 30, 32, 34, 35, 36, 43, 44, 45, 46, 47, 48, 49, 51, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 70, 71, 72], "white": [1, 2, 29, 49, 50, 54], "given": [1, 2, 6, 15, 16, 20, 21, 23, 25, 26, 29, 31, 40, 42, 46, 49, 50, 51, 57, 62, 63, 67, 73], "g1": 1, "g2": 1, "distribut": [1, 2, 10, 11, 12, 15, 16, 18, 21, 22, 23, 25, 27, 30, 32, 39, 40, 45, 48, 49, 50, 52, 53, 56, 59, 62, 64, 67, 69], "p": [1, 2, 5, 11, 12, 14, 15, 16, 18, 19, 20, 21, 22, 23, 25, 29, 31, 32, 45, 46, 47, 49, 50, 51, 54, 56, 57, 62, 67, 69, 72, 73], "q": [1, 15, 16, 19, 21, 22, 25, 27, 35, 46, 49, 54, 69], "n": [1, 2, 5, 11, 14, 15, 16, 18, 19, 20, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 34, 35, 38, 40, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 64, 67, 69, 71, 73], "0": [1, 2, 4, 9, 10, 14, 15, 16, 20, 21, 22, 23, 25, 27, 29, 31, 32, 34, 35, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73], "knm": 1, "\u00b9": [1, 19, 21, 54], "And": [1, 43, 46, 49, 55, 56, 58, 59, 60, 61, 62, 63, 65], "q_sqrt\u1d40": [1, 27, 54], "thi": [1, 2, 3, 4, 5, 7, 9, 10, 11, 12, 14, 15, 16, 19, 20, 21, 22, 23, 24, 25, 27, 29, 30, 32, 34, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74], "method": [1, 3, 9, 11, 16, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 32, 34, 35, 38, 40, 42, 44, 45, 46, 47, 50, 51, 52, 55, 56, 60, 62, 67, 68, 69, 70, 71, 74], "comput": [1, 5, 9, 14, 15, 16, 18, 20, 21, 22, 23, 25, 27, 29, 31, 32, 34, 38, 41, 46, 48, 49, 50, 52, 54, 55, 56, 62, 63, 64, 66, 69, 71, 72, 73], "mean": [1, 2, 5, 6, 7, 9, 10, 14, 15, 16, 18, 21, 22, 23, 25, 27, 29, 31, 32, 39, 40, 42, 44, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 62, 63, 65, 66, 67, 69, 71, 72, 73, 74], "co": [1, 14, 29, 47, 48, 49, 51, 54, 70], "varianc": [1, 2, 9, 10, 14, 16, 20, 21, 22, 23, 25, 29, 32, 34, 42, 44, 45, 48, 49, 50, 51, 52, 54, 57, 58, 59, 62, 63, 64, 66, 67, 68, 69, 70, 72, 73], "paramet": [1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 39, 40, 42, 43, 44, 45, 46, 48, 51, 54, 55, 57, 59, 60, 64, 66, 67, 68, 70, 71, 73, 74], "option": [1, 2, 3, 5, 6, 9, 10, 11, 12, 13, 14, 16, 20, 21, 22, 23, 25, 27, 29, 30, 32, 34, 35, 36, 40, 42, 44, 45, 49, 50, 51, 53, 54, 55, 62, 65, 66, 67, 68, 70, 71, 72], "tensor": [1, 2, 4, 5, 6, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 34, 35, 36, 47, 49, 51, 54, 55, 56, 57, 60, 61, 62, 63, 65, 66, 67, 68], "ha": [1, 2, 3, 9, 10, 14, 15, 16, 18, 19, 20, 21, 22, 23, 25, 27, 29, 31, 32, 34, 35, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73], "shape": [1, 2, 10, 11, 12, 14, 15, 16, 18, 19, 20, 21, 22, 23, 25, 27, 29, 30, 31, 32, 34, 35, 42, 44, 45, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72], "m_r_or_r_m_m": [1, 2], "If": [1, 5, 10, 14, 16, 21, 23, 25, 27, 29, 34, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 59, 60, 64, 65, 66, 67, 68, 70, 71, 72, 74], "i": [1, 2, 3, 5, 7, 8, 9, 10, 11, 12, 14, 15, 16, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74], "must": [1, 16, 19, 21, 26, 32, 34, 48, 55, 60, 62, 63, 66, 67], "have": [1, 9, 11, 14, 16, 27, 32, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74], "r": [1, 2, 14, 20, 21, 38, 45, 51], "m": [1, 2, 11, 12, 14, 15, 16, 21, 22, 23, 25, 28, 34, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 59, 65, 66, 67, 69, 70, 71, 72, 73], "lower": [1, 3, 15, 16, 19, 20, 21, 22, 23, 25, 27, 34, 42, 47, 51, 52, 53, 54, 67, 70, 72, 74], "triangular": [1, 15, 19, 27, 54], "diagon": [1, 3, 10, 14, 15, 21, 34, 52, 56, 66, 73], "batch": [1, 2, 14, 16, 20, 21, 22, 23, 25, 29, 31, 32, 34, 35, 52, 62, 65], "bool": [1, 2, 10, 14, 15, 20, 21, 22, 23, 25, 27, 29, 32, 34, 49, 50, 58, 60, 62], "return": [1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 44, 47, 49, 51, 53, 54, 55, 56, 57, 58, 60, 61, 62, 64, 65, 66, 67, 68, 71, 72], "type": [1, 2, 3, 4, 5, 6, 8, 9, 10, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 51, 54, 55, 57, 62, 63, 65, 67, 74], "tupl": [1, 2, 5, 9, 11, 12, 14, 16, 20, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 34, 47, 55, 63, 64, 65, 67], "1": [1, 2, 5, 9, 11, 12, 14, 16, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 38, 40, 42, 43, 44, 45, 46, 47, 48, 50, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73], "us": [1, 2, 3, 4, 5, 9, 10, 11, 14, 15, 16, 19, 20, 21, 22, 23, 25, 26, 27, 29, 30, 32, 34, 35, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74], "multipl": [1, 4, 5, 11, 14, 15, 16, 20, 21, 29, 34, 48, 49, 51, 61, 62, 63, 67, 69, 73, 74], "dispatch": [1, 4, 5, 15, 29, 51, 65], "which": [1, 2, 4, 10, 11, 14, 15, 16, 18, 19, 20, 21, 22, 23, 25, 26, 27, 29, 30, 34, 35, 40, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 55, 56, 57, 58, 59, 60, 61, 62, 64, 66, 67, 69, 70, 71], "depend": [1, 4, 6, 9, 14, 15, 25, 29, 33, 41, 46, 48, 55, 66, 67, 69], "argument": [1, 4, 14, 15, 26, 27, 29, 32, 42, 45, 47, 49, 54, 58, 62, 66], "pass": [1, 4, 5, 10, 15, 21, 24, 26, 27, 29, 32, 34, 35, 42, 48, 51, 55, 57, 58, 61, 62, 64, 65, 66, 68], "object": [1, 3, 4, 10, 11, 14, 15, 16, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 32, 34, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 57, 60, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 74], "inducingvari": [1, 5, 6, 12, 15, 21, 23, 24, 29, 51, 54], "kernel": [1, 4, 5, 6, 10, 11, 15, 20, 21, 22, 23, 25, 26, 27, 29, 38, 39, 40, 42, 43, 46, 47, 49, 50, 53, 54, 55, 56, 57, 59, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 74], "_sparse_condit": 1, "xnew": [1, 4, 20, 21, 22, 23, 25, 29, 46, 54, 56, 57, 61, 63, 71], "inducing_vari": [1, 4, 5, 6, 10, 15, 21, 22, 23, 24, 29, 42, 44, 47, 48, 49, 50, 51, 52, 54, 57, 59, 65, 68, 70, 71, 72], "full_output_cov": [1, 2, 14, 20, 21, 22, 23, 25, 29, 54], "singl": [1, 2, 14, 15, 16, 21, 26, 32, 35, 43, 48, 51, 52, 53, 55, 58, 62, 67, 72], "output": [1, 2, 3, 11, 12, 14, 16, 21, 22, 23, 25, 28, 32, 35, 40, 45, 48, 49, 53, 54, 56, 57, 58, 61, 62, 64, 65, 67, 69, 73, 74], "gp": [1, 2, 9, 11, 14, 16, 20, 21, 22, 23, 25, 38, 44, 45, 47, 51, 52, 53, 54, 55, 66, 68, 69, 70, 74], "The": [1, 2, 3, 8, 9, 10, 11, 14, 15, 16, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 32, 34, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 59, 60, 61, 63, 64, 65, 69, 70, 71, 72, 73, 74], "covari": [1, 2, 10, 11, 14, 15, 16, 18, 21, 23, 25, 27, 30, 40, 45, 46, 51, 52, 54, 58, 64, 65, 66, 69, 73, 74], "matric": [1, 3, 10, 14, 20, 22, 23, 25, 54, 58, 67, 69], "calcul": [1, 2, 5, 14, 21, 22, 27, 32, 46, 47, 51, 67], "follow": [1, 11, 16, 31, 32, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 58, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74], "kuu": [1, 11, 14, 51, 54, 65], "kuf": [1, 11, 14, 51, 54, 65], "kff": 1, "further": [1, 2, 56, 62, 64, 69], "refer": [1, 2, 14, 16, 21, 22, 23, 40, 51, 54, 59, 66, 68, 73], "see": [1, 2, 3, 9, 10, 14, 20, 21, 22, 23, 25, 27, 29, 34, 37, 39, 40, 42, 45, 47, 48, 49, 51, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 67, 68, 69, 71, 72, 74], "_dense_condit": 1, "below": [1, 37, 40, 49, 55, 56, 57, 58, 62, 63, 66, 69, 71], "detail": [1, 2, 10, 37, 39, 47, 49, 51, 56, 57, 62, 65, 66, 68, 69, 74], "explan": [1, 2], "case": [1, 2, 3, 9, 14, 15, 26, 27, 32, 40, 45, 46, 50, 51, 54, 55, 56, 59, 60, 61, 62, 66, 70, 72, 74], "multiouput": [1, 51], "notebook": [1, 2, 3, 10, 14, 16, 21, 22, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 54, 55, 57, 59, 62, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74], "more": [1, 2, 3, 10, 11, 14, 16, 20, 21, 22, 23, 25, 32, 37, 40, 42, 43, 45, 46, 49, 50, 51, 54, 55, 56, 58, 59, 60, 62, 66, 67, 68, 69, 72, 74], "inform": [1, 2, 14, 38, 42, 44, 45, 56, 67, 69], "about": [1, 2, 14, 16, 37, 41, 48, 56, 57, 58, 60, 62, 63], "framework": [1, 2, 30, 38, 40, 51, 61, 63, 64, 67, 74], "d": [1, 2, 5, 11, 12, 14, 18, 20, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 34, 35, 38, 42, 44, 45, 47, 51, 52, 54, 56, 64, 69, 73], "data": [1, 3, 9, 14, 16, 20, 21, 22, 23, 25, 29, 30, 34, 35, 38, 39, 40, 44, 46, 52, 53, 54, 56, 60, 62, 63, 64, 65, 67, 68, 69, 70, 71, 73, 74], "matrix": [1, 14, 15, 18, 19, 21, 28, 34, 45, 50, 51, 54, 56, 58, 66, 69, 73], "between": [1, 2, 11, 14, 15, 16, 21, 23, 25, 28, 30, 35, 38, 43, 45, 46, 47, 51, 52, 55, 56, 57, 58, 62, 68, 69, 72, 73], "datapoint": [1, 14], "note": [1, 2, 5, 11, 14, 15, 16, 21, 22, 27, 35, 40, 44, 45, 46, 48, 49, 50, 51, 52, 54, 58, 59, 64, 66, 69, 72, 73], "we": [1, 5, 9, 10, 11, 14, 15, 16, 18, 19, 20, 21, 26, 30, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74], "ar": [1, 2, 3, 5, 6, 9, 10, 11, 14, 15, 16, 20, 21, 22, 23, 25, 26, 27, 32, 34, 35, 37, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74], "repetit": [1, 2, 31], "zero": [1, 3, 14, 22, 34, 35, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 58, 60, 66, 67, 71], "standard": [1, 3, 9, 21, 27, 49, 52, 55, 57, 64], "deviat": [1, 9, 53, 64], "choleski": [1, 2, 15, 18, 21, 27, 49, 64, 73], "size": [1, 11, 12, 14, 16, 21, 29, 32, 47, 48, 49, 50, 52, 53, 54, 59, 64, 67, 71], "boolean": [1, 14], "whether": [1, 6, 14, 27, 34, 44, 46, 54, 62, 69], "whiten": [1, 2, 15, 21, 23, 25, 29, 50, 54, 70], "represent": [1, 2, 10, 21, 25, 27, 54, 70], "broadcast": [1, 14, 15, 16, 18, 28, 32, 34], "x": [1, 5, 9, 14, 15, 16, 17, 18, 20, 21, 22, 23, 25, 29, 31, 32, 34, 35, 36, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 69, 70, 71, 72], "repres": [1, 9, 14, 15, 16, 21, 27, 29, 30, 31, 32, 35, 48, 49, 51, 54, 55, 59, 62, 67, 69], "point": [1, 2, 5, 11, 14, 16, 20, 21, 22, 23, 25, 29, 30, 31, 32, 35, 38, 42, 44, 45, 46, 47, 49, 50, 52, 54, 55, 56, 57, 62, 64, 65, 66, 68, 69, 70, 72, 73, 74], "produc": [1, 14, 19, 21, 22, 67, 71], "addition": [1, 9, 73], "mai": [1, 9, 16, 21, 22, 35, 40, 41, 55, 56, 57, 58, 59, 60, 62], "gaussian": [1, 9, 14, 20, 21, 22, 25, 27, 29, 31, 32, 34, 38, 39, 40, 45, 46, 47, 48, 49, 52, 53, 54, 56, 59, 64, 66, 67, 68, 69, 70, 73, 74], "uncertainti": [1, 16, 40, 45, 47, 55, 56, 57], "In": [1, 9, 11, 14, 15, 16, 19, 32, 38, 40, 44, 46, 47, 48, 49, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 70, 72, 74], "squar": [1, 14, 15, 21, 42, 54, 58, 62, 64, 73], "root": [1, 15, 54, 67], "been": [1, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 58, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72], "center": [1, 21, 49, 53, 55, 59, 67, 68], "so": [1, 14, 16, 21, 26, 27, 35, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72], "v": [1, 19, 21, 22, 27, 45, 49, 65, 67, 71], "\ud835\udca9": 1, "\ud835\udfce": 1, "\ud835\udc08": 1, "\ud835\udc0bv": 1, "thu": [1, 55], "\ud835\udc0b\ud835\udc0b\u1d40": 1, "\ud835\udc0a": 1, "taken": [1, 32, 47, 73], "can": [1, 2, 3, 9, 10, 11, 14, 15, 16, 19, 21, 22, 26, 27, 29, 32, 35, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 71, 72, 73, 74], "either": [1, 3, 10, 14, 15, 24, 49, 56, 57, 61, 62], "each": [1, 9, 11, 14, 15, 16, 22, 26, 27, 34, 35, 42, 45, 46, 47, 48, 49, 51, 55, 56, 58, 64, 67, 68], "default": [1, 3, 9, 10, 16, 20, 21, 22, 23, 24, 25, 26, 27, 29, 32, 34, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 62, 64, 65, 66, 67, 68, 70, 71, 72, 74], "full": [1, 3, 14, 21, 23, 25, 27, 40, 45, 46, 49, 58, 60, 62, 69, 70, 73], "true": [1, 10, 14, 21, 23, 25, 27, 29, 32, 34, 42, 44, 45, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 70, 71, 72], "assum": [1, 9, 14, 15, 16, 19, 21, 23, 25, 32, 35, 39, 42, 45, 51, 54, 55, 56, 57, 58, 62, 66, 74], "independ": [1, 2, 9, 11, 14, 15, 20, 21, 23, 25, 32, 48, 50, 68, 73, 74], "column": [1, 9, 14, 15, 20, 21, 45, 55, 62, 69], "first": [1, 8, 10, 15, 16, 28, 32, 34, 41, 45, 46, 47, 49, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 67, 68, 69, 71, 72, 74], "dimens": [1, 11, 12, 14, 15, 16, 21, 28, 29, 30, 31, 32, 35, 42, 45, 51, 54, 56, 66, 67], "evalu": [1, 10, 14, 16, 21, 27, 32, 44, 46, 47, 51, 66, 67, 69], "new": [1, 3, 10, 11, 20, 21, 22, 34, 40, 41, 51, 54, 56, 57, 58, 62, 63, 64, 66, 67, 69, 74], "describ": [1, 14, 16, 40, 43, 48, 51, 60], "abov": [1, 2, 21, 27, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73], "sharedindependentinducingvari": [1, 4, 29, 51], "sharedindepend": [1, 4, 11, 29, 51, 54], "multioutput": [1, 2, 4, 11, 14, 38, 51], "shared_independent_condit": [1, 51], "share": [1, 11, 14, 21, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 64, 65, 66, 67, 68, 70, 71, 72], "induc": [1, 2, 6, 11, 12, 14, 22, 38, 40, 42, 46, 47, 49, 50, 52, 54, 57, 68, 69, 70, 72, 74], "same": [1, 2, 10, 11, 14, 22, 26, 27, 32, 34, 46, 48, 49, 51, 53, 55, 56, 57, 58, 59, 61, 63, 64, 65, 69, 70, 72], "behaviour": [1, 14, 46, 58, 74], "non": [1, 9, 16, 21, 24, 34, 38, 40, 44, 49, 62, 65, 73, 74], "_condit": [1, 2], "l": [1, 2, 11, 14, 15, 18, 19, 21, 22, 27, 38, 43, 44, 45, 46, 47, 51, 54, 64, 67, 68, 69, 71], "m_l_or_l_m_m": [1, 2, 15, 29], "pleas": [1, 27, 35, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 58, 64, 65, 66, 67, 68, 70, 71, 72], "_expand_independent_output": 1, "separateindependentinducingvari": [1, 4, 29, 48, 51], "separateindepend": [1, 4, 11, 29, 48, 51, 54], "separate_independent_condit": [1, 51], "multioutputinducingvari": 1, "multioutputkernel": [1, 4, 29, 51], "fallbacksharedindependentinducingvari": [1, 4, 29, 51], "independentlat": [1, 4, 11, 29, 51], "fallbackseparateindependentinducingvari": [1, 4, 29, 51], "fallback_independent_latent_condit": [1, 51], "interdomain": [1, 2, 38, 51], "latent": [1, 2, 9, 11, 14, 16, 21, 22, 23, 25, 35, 38, 40, 49, 50, 51, 53, 74], "number": [1, 2, 3, 5, 10, 11, 12, 14, 16, 19, 21, 22, 26, 30, 31, 32, 34, 35, 40, 42, 43, 44, 45, 47, 48, 50, 51, 53, 54, 56, 59, 62, 64, 67, 68, 71, 72, 73], "differ": [1, 5, 9, 11, 14, 15, 16, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 55, 56, 57, 58, 59, 62, 63, 67, 68, 71, 72], "than": [1, 9, 16, 21, 44, 45, 46, 50, 52, 56, 58, 59, 71, 72, 74], "inducingpoint": [1, 4, 21, 22, 24, 29, 44, 48, 51, 65], "inducing_point_condit": [1, 51], "multi": [1, 2, 11, 12, 14, 16, 40, 45, 49, 54, 67, 74], "fulli": [1, 2, 16, 45, 51, 65, 68, 74], "correl": [1, 2, 14, 21, 45, 51], "variabl": [1, 3, 4, 5, 6, 9, 10, 11, 12, 14, 15, 16, 18, 19, 20, 21, 22, 23, 25, 27, 29, 30, 31, 32, 34, 36, 38, 40, 44, 46, 48, 49, 53, 54, 56, 59, 62, 63, 64, 66, 67, 69, 70, 71, 74], "wai": [1, 3, 11, 40, 41, 46, 52, 57, 58, 61, 62, 63, 73, 74], "k": [1, 9, 14, 15, 16, 19, 20, 21, 22, 23, 25, 34, 38, 43, 45, 47, 48, 49, 50, 51, 53, 54, 55, 65, 71, 73], "allow": [1, 2, 5, 9, 11, 14, 16, 20, 21, 22, 23, 24, 25, 27, 29, 34, 42, 43, 45, 49, 51, 55, 57, 58, 61, 62, 63, 66, 67], "scheme": [1, 49], "variat": [1, 11, 12, 16, 20, 21, 22, 23, 25, 26, 27, 30, 32, 38, 48, 49, 51, 68, 69, 70, 73, 74], "l_1_or_1_l_l": 1, "linearcoregion": [1, 4, 11, 29, 51], "coregionalization_condit": [1, 51], "most": [1, 11, 21, 27, 29, 32, 40, 49, 51, 56, 58, 61, 67, 74], "effici": [1, 11, 14, 20, 21, 22, 23, 25, 45, 47, 51, 52, 54, 69, 73], "routin": [1, 16, 51], "project": [1, 21, 35, 39, 40, 44, 51, 54, 58, 72], "through": [1, 10, 14, 20, 21, 22, 23, 25, 26, 27, 29, 32, 34, 40, 49, 56, 57, 58, 62, 64, 72], "mix": [1, 2, 14, 74], "w": [1, 2, 9, 14, 20, 21, 32, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 64, 65, 66, 67, 68, 70, 71, 72], "member": 1, "_sample_condit": 1, "num_sampl": [1, 2, 21, 27, 49, 58, 61], "sampl": [1, 2, 16, 18, 21, 32, 40, 43, 48, 49, 55, 57, 58, 60, 64, 66, 67, 74], "from": [1, 2, 3, 9, 11, 14, 15, 16, 19, 20, 21, 22, 23, 25, 27, 29, 31, 34, 35, 40, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73], "sqrt": [1, 45, 48, 51, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 66, 70, 71], "ep": [1, 40], "howev": [1, 11, 21, 49, 54, 58, 59, 60, 61, 62, 63, 67, 71, 72], "some": [1, 9, 11, 12, 16, 21, 22, 26, 30, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 59, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73], "combin": [1, 5, 11, 13, 40, 45, 49, 52, 57, 58, 60, 61, 65, 73, 74], "mok": 1, "mof": 1, "exist": [1, 26, 34, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 58, 63, 64, 65, 66, 67, 68, 70, 71, 72], "make": [1, 3, 16, 27, 29, 34, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74], "sure": [1, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 62, 64, 65, 66, 67, 68, 70, 71, 72], "effic": 1, "one": [1, 5, 9, 11, 14, 16, 21, 29, 32, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 57, 58, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73], "2": [1, 5, 9, 10, 14, 15, 16, 19, 20, 21, 22, 34, 35, 41, 42, 43, 44, 45, 46, 47, 48, 50, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73], "cov": [1, 2, 14, 22, 30, 32, 43, 45, 49, 50, 53, 54, 64], "maybe_r": 1, "int": [1, 2, 3, 5, 8, 9, 10, 11, 12, 14, 16, 19, 20, 21, 22, 23, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 47, 49, 50, 65, 67, 69, 73], "xnew_mu": 1, "xnew_var": 1, "q_mu": [1, 15, 21, 23, 27, 29, 44, 48, 50, 51, 52, 54, 57], "mean_funct": [1, 20, 21, 22, 23, 25, 29, 49, 60, 64], "uncertain": 1, "input": [1, 2, 9, 11, 12, 14, 16, 20, 21, 23, 25, 28, 30, 31, 32, 34, 35, 38, 42, 45, 47, 48, 49, 51, 53, 54, 55, 56, 58, 64, 65, 67, 68, 69], "document": [1, 7, 10, 27, 41, 51, 58, 60, 73, 74], "din": [1, 32], "t": [1, 14, 16, 20, 21, 24, 30, 34, 38, 40, 43, 44, 46, 49, 50, 52, 54, 55, 57, 58, 59, 60, 61, 64, 65, 66, 67], "onli": [1, 5, 9, 11, 14, 16, 20, 21, 22, 23, 25, 27, 29, 30, 32, 42, 48, 49, 50, 51, 52, 55, 56, 59, 60, 62, 63, 64, 66, 67, 72, 73], "support": [1, 10, 21, 27, 40, 51, 58, 67], "dout": [1, 32], "wheter": 1, "influenc": 1, "fvar": [1, 2, 16, 32, 54], "meanfunct": [1, 5, 6, 20, 21, 22, 23, 25, 29, 60], "fmean": [1, 54, 57], "lm": 2, "base_condit": [2, 51], "except": [2, 67], "instead": [2, 14, 15, 34, 35, 41, 42, 46, 47, 48, 49, 51, 54, 55, 56, 57, 58, 60, 61, 63, 65, 67, 68], "accept": [2, 26], "decomposit": [2, 18, 49, 73], "precomput": [2, 20, 22, 23, 25, 29, 54], "improv": [2, 27, 40], "perform": [2, 16, 27, 31, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 57, 58, 59, 64, 65, 66, 67, 68, 70, 71, 72, 73], "reshap": [2, 44, 53, 54, 55, 58, 59, 65, 66, 67, 71], "correct": [2, 14, 52, 54, 65, 69], "specifi": [2, 9, 11, 14, 16, 24, 26, 27, 32, 40, 45, 51, 54, 55, 60, 64, 67], "handl": [2, 3, 10, 14, 27, 58, 66, 73], "where": [2, 9, 11, 12, 14, 16, 19, 20, 21, 27, 30, 32, 34, 35, 43, 44, 45, 46, 49, 50, 51, 53, 54, 55, 57, 58, 59, 60, 64, 66, 67, 69, 70, 72, 73], "all": [2, 3, 9, 10, 11, 21, 26, 27, 28, 31, 32, 34, 40, 42, 45, 49, 51, 54, 55, 56, 57, 58, 61, 62, 63, 64, 65, 66, 67, 69, 70, 72, 74], "both": [2, 9, 10, 15, 26, 41, 48, 49, 51, 56, 62, 67], "prior": [2, 10, 14, 20, 21, 27, 34, 39, 40, 42, 44, 48, 50, 51, 54, 55, 57, 59, 64, 66, 67, 69, 72, 73], "posterior": [2, 10, 20, 21, 22, 23, 25, 45, 47, 49, 50, 51, 52, 54, 67, 69, 70, 74], "_1_l_or_1_m_m": 2, "live": [2, 51], "g": [2, 14, 16, 20, 21, 22, 23, 25, 35, 38, 40, 44, 47, 49, 68], "space": [2, 11, 14, 42, 48, 49, 59, 64, 65], "g_mean": 2, "g_var": 2, "take": [2, 9, 11, 16, 21, 27, 30, 32, 34, 44, 45, 49, 51, 52, 54, 57, 58, 60, 61, 62, 64, 65, 66, 67, 73], "uncorrel": [2, 14, 21], "dimension": [2, 14, 16, 31, 35, 38, 42, 43, 53, 54, 59, 66, 73, 74], "f_mean": [2, 55, 56, 58, 60], "f_var": [2, 55, 56, 58, 60], "A": [2, 9, 10, 14, 16, 19, 21, 22, 26, 27, 29, 35, 38, 40, 42, 47, 49, 50, 51, 52, 54, 58, 59, 60, 62, 64, 68, 69, 70, 73, 74], "num_rol": 2, "roll": 2, "backward": [2, 9, 20, 22, 23, 25], "time": [2, 8, 32, 37, 44, 45, 46, 47, 51, 56, 58, 61, 62, 63, 64, 66, 67, 69], "left": [2, 16, 54, 62, 67, 73], "right": [2, 16, 47, 54, 58, 62, 63, 67, 73], "forward": [2, 27], "multivari": [2, 16, 18, 21, 25, 31, 32, 49], "normal": [2, 16, 18, 31, 35, 44, 45, 48, 49, 51, 57, 62, 63, 64, 67], "": [2, 9, 10, 14, 18, 20, 21, 22, 23, 24, 25, 26, 27, 29, 32, 34, 40, 42, 44, 45, 46, 47, 48, 49, 52, 54, 55, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 72, 73, 74], "mvn": 2, "process": [2, 9, 11, 14, 16, 20, 21, 25, 38, 39, 40, 45, 46, 47, 48, 49, 54, 56, 59, 62, 63, 64, 66, 67, 68, 69, 70, 73, 74], "equal": [2, 21, 48, 64, 67], "privat": 3, "modul": [3, 9, 29, 49, 57, 63], "manag": [3, 14, 59, 63], "configur": [3, 27, 40, 56, 57, 61, 62], "provid": [3, 10, 11, 16, 20, 21, 22, 23, 25, 26, 32, 49, 51, 54, 57, 61, 67, 74], "modifi": 3, "set": [3, 5, 10, 11, 14, 20, 22, 23, 25, 26, 27, 29, 33, 34, 37, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 63, 64, 65, 66, 67, 68, 70, 71, 72], "float": [3, 4, 10, 11, 12, 14, 16, 19, 20, 21, 22, 24, 26, 27, 34, 35, 36, 44, 53, 60, 61, 62, 65, 71], "precis": [3, 21, 44, 51, 52], "integ": [3, 9, 10, 16, 21, 31, 42, 45, 54], "posit": [3, 10, 14, 15, 19, 21, 24, 35, 45, 48, 49, 54, 55, 59, 62, 66, 67, 71, 73], "transform": [3, 10, 14, 16, 27, 34, 42, 44, 48, 49, 50, 51, 52, 54, 55, 57, 59, 66, 67, 72], "minimum": [3, 14, 66], "shift": [3, 42, 44, 51, 54, 55, 57, 59, 62, 66, 72], "format": [3, 42, 54, 62, 64, 65], "print_summari": [3, 42, 44, 49, 50, 51, 54, 55, 57, 59, 62, 66, 67, 72], "hold": [3, 14, 21, 62], "global": 3, "store": [3, 9, 20, 22, 23, 25, 26, 29, 34, 57, 62, 63, 67], "environ": [3, 55], "altern": [3, 41, 45, 49, 59, 62], "chang": [3, 7, 14, 20, 22, 23, 25, 29, 42, 47, 48, 50, 62, 63, 69, 74], "user": [3, 16, 38, 39, 40, 49, 51, 58, 59, 64, 66], "befor": [3, 44, 47, 49, 52, 56, 57, 58, 61, 62, 63], "run": [3, 19, 21, 26, 35, 37, 42, 43, 44, 45, 46, 49, 51, 52, 53, 54, 61, 62, 64, 65, 66, 67, 68, 70, 71, 72], "python": [3, 16, 27, 34, 39, 40, 48, 51, 61, 62, 63, 67, 68], "interpret": [3, 57], "avail": [3, 5, 16, 26, 37, 49, 51, 60, 64, 67, 73, 74], "gpflow_int": 3, "int16": 3, "int32": [3, 57], "int64": 3, "gpflow_float": 3, "float16": 3, "float32": 3, "float64": [3, 42, 44, 45, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 61, 62, 63, 64, 66, 67, 71, 72], "gpflow_positive_bijector": 3, "exp": [3, 14, 16, 32, 48, 49, 50, 53, 54, 62, 67], "softplu": [3, 10, 44, 48, 51, 63], "gpflow_positive_minimum": 3, "ani": [3, 4, 5, 6, 8, 9, 10, 11, 12, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 40, 49, 51, 57, 58, 60, 62, 63, 64, 67, 72], "gpflow_summary_fmt": 3, "other": [3, 10, 14, 16, 21, 23, 25, 26, 35, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 59, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74], "tabul": 3, "gpflow_jitt": 3, "also": [3, 10, 14, 21, 27, 40, 42, 44, 48, 49, 51, 54, 56, 57, 58, 59, 62, 63, 67, 69, 72, 74], "temporarili": 3, "context": [3, 29, 30, 52, 62, 64], "jitter": [3, 4, 10, 50, 54, 64, 65], "1e": [3, 16, 44, 49, 50, 58, 60, 64, 66, 68], "5": [3, 10, 14, 21, 22, 26, 35, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73], "code": [3, 7, 11, 14, 21, 33, 34, 41, 44, 51, 54, 62, 63, 65, 67, 69, 72, 73], "here": [3, 11, 14, 16, 21, 22, 41, 44, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 70, 72], "factori": [3, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "positive_bijector": 3, "positive_minimum": 3, "summary_fmt": 3, "base": [3, 9, 10, 11, 12, 14, 16, 19, 20, 21, 22, 23, 25, 26, 27, 29, 30, 32, 34, 40, 45, 51, 54, 55, 56, 57, 59, 60, 62, 63, 66, 67], "immut": 3, "str": [3, 10, 11, 12, 13, 14, 26, 27, 29, 33, 34, 49, 50, 54, 65], "mainli": [3, 51, 67], "badli": 3, "condit": [3, 10, 11, 14, 16, 22, 46, 47, 51, 54, 68, 69, 74], "stabl": [3, 69, 73], "6": [3, 16, 22, 35, 38, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72], "bijector": [3, 10, 16, 34, 44, 48, 49, 62], "bound": [3, 8, 16, 20, 21, 22, 23, 25, 34, 38, 42, 44, 51, 52, 54, 70, 73, 74], "summari": [3, 34, 62], "print": [3, 8, 10, 34, 42, 44, 45, 47, 48, 49, 52, 54, 61, 62, 63, 64, 65, 67, 68, 70, 72], "temporary_config": 3, "ensur": [3, 14, 21, 48, 49, 62, 67, 73], "test": [3, 14, 44, 46, 47, 54, 56, 61, 63, 64, 68], "gener": [3, 9, 11, 14, 21, 34, 42, 45, 53, 56, 57, 58, 59, 60, 61, 62, 63, 65], "current": [3, 14, 21, 26, 27, 40, 51, 63, 64, 71], "activ": [3, 14, 44, 51, 64, 65, 67], "constraint": [3, 10, 11, 62], "constant": [3, 10, 14, 16, 21, 34, 43, 48, 49, 55, 58, 60, 66, 74], "add": [3, 10, 21, 35, 45, 46, 49, 55, 58, 60, 63, 66, 72], "understood": 3, "special": [3, 51, 70, 74], "dict": [3, 27, 34, 42, 45, 49, 50, 51, 53, 54, 55, 62, 65, 67, 68, 70, 71, 72], "new_config": 3, "updat": [3, 20, 21, 22, 23, 25, 29, 34, 44, 48, 51, 52, 62, 63, 65], "value_typ": 3, "np": [3, 22, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 70, 71, 72], "achiev": [3, 10, 14, 51, 52, 60, 64, 67], "numer": [3, 10, 16, 19, 21, 62, 67, 73], "stabil": [3, 10, 67], "system": [3, 10, 38, 42, 44, 45, 60, 67], "when": [3, 5, 7, 10, 16, 19, 20, 21, 22, 23, 25, 27, 29, 35, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 62, 63, 64, 65, 66, 67, 68, 71, 72, 73, 74], "associ": [3, 10, 16, 22, 42, 45], "larg": [3, 10, 14, 21, 22, 39, 40, 47, 52, 55, 74], "therefor": [3, 10, 14, 16, 51, 65], "nearli": [3, 10], "singular": [3, 10], "There": [3, 14, 21, 40, 46, 51, 60, 62], "two": [3, 10, 14, 16, 41, 42, 43, 45, 46, 48, 50, 51, 55, 56, 57, 58, 59, 62, 63, 66, 67, 68, 69, 73, 74], "implement": [3, 5, 9, 11, 14, 16, 20, 21, 22, 25, 26, 27, 32, 34, 35, 37, 42, 43, 45, 48, 52, 54, 57, 58, 60, 61, 64, 66, 69, 73, 74], "kuf_kernel_inducingpoint": 4, "union": [4, 5, 6, 9, 10, 11, 12, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36], "ndarrai": [4, 5, 6, 9, 10, 11, 12, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 27, 29, 30, 31, 32, 34, 36], "multiscal": 4, "squaredexponenti": [4, 14, 44, 46, 47, 48, 49, 50, 51, 53, 55, 56, 57, 58, 59, 61, 62, 63, 65, 68, 70, 71, 72], "kuf_sqexp_multiscal": 4, "inducingpatch": [4, 44], "convolut": [4, 38, 40, 74], "kuf_conv_patch": 4, "kuf_gener": 4, "kuf_shared_shar": 4, "kuf_separate_shar": 4, "kuf_shared_separ": 4, "kuf_separate_separ": 4, "kuf_fallback_separate_linear_coregion": 4, "kuf_fallback_shared_linear_coregion": 4, "kuf_shared_linear_coregion": 4, "kuf_separate_linear_coregion": 4, "kuu_kernel_inducingpoint": 4, "kuu_sqexp_multiscal": 4, "kuu_conv_patch": 4, "kuu_gener": 4, "kuu_shared_shar": 4, "kuu_fallback_shar": 4, "kuu_fallback_separate_shar": 4, "kuu_fallbace_separ": 4, "quadratur": [5, 10, 16, 73], "obj1": 5, "obj2": 5, "nghp": 5, "_p": 5, "select": [5, 21, 34, 47, 59], "analyt": [5, 27, 40, 52, 57], "fall": [5, 51, 55], "back": [5, 27, 43, 51, 60, 63, 73], "_quadrature_expect": 5, "gauss": [5, 16, 31, 32], "hermit": [5, 16, 31, 32], "num_gauss_hermite_point": 5, "3": [5, 9, 10, 14, 16, 22, 26, 34, 35, 42, 43, 44, 45, 46, 47, 48, 50, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72], "contain": [5, 7, 15, 16, 20, 21, 22, 23, 25, 27, 34, 42, 43, 45, 48, 49, 51, 54, 57, 67, 69, 73], "psi": 5, "statist": [5, 16, 38, 42, 49], "ekdiag": 5, "psi0": 5, "ekxz": 5, "nxm": 5, "psi1": 5, "exkxz": 5, "identity_mean": 5, "nxdxm": 5, "ekzxkxz": 5, "nxmxm": 5, "psi2": 5, "ekzxmx": 5, "nxmxq": 5, "emxkxz": 5, "nxqxm": 5, "emx": 5, "nxq": 5, "em1x_m2x": 5, "mean1": 5, "mean2": 5, "nxq1xq2": 5, "1xq": 5, "row": [5, 9, 14, 53, 56], "vector": [5, 16, 19, 21, 25, 54, 56, 58, 66, 71], "occur": [5, 27, 43], "instanc": [5, 10, 21, 26, 27, 34, 46, 51, 60, 62, 63, 64, 67], "sum": [5, 9, 15, 16, 21, 50], "ek1zxk2xz": 5, "kern1": 5, "kern2": 5, "probabilitydistribut": 5, "approxim": [5, 11, 16, 19, 21, 22, 25, 32, 38, 40, 47, 48, 49, 51, 52, 54, 59, 62, 69, 70, 72, 73, 74], "integr": [5, 16, 20, 21, 32, 62, 69, 73], "obj": [6, 47], "slice": [6, 14], "interest": [6, 14, 40, 56, 57, 58, 66, 67, 74], "callabl": [6, 8, 16, 21, 26, 27, 28, 32, 34, 35, 63, 67], "packag": [7, 21, 40, 48, 51, 67], "still": [7, 48, 51, 52, 54, 56, 58, 59], "expect": [7, 10, 16, 19, 21, 30, 31, 32, 47, 48, 53, 56, 60, 63, 65, 67, 71, 73], "break": [7, 44], "poor": [7, 22], "bug": [7, 40], "consid": [7, 35, 45, 46, 48, 49, 51, 73], "matur": 7, "move": [7, 35, 60], "out": [7, 21, 32, 41, 62, 63, 68], "func": [8, 32, 34, 47, 65], "decor": [8, 51], "mark": [8, 38, 40, 44, 51, 62, 72], "call": [8, 11, 16, 20, 22, 23, 25, 27, 29, 32, 34, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 58, 60, 61, 62, 64, 65, 66, 67, 68, 70, 71, 72], "warn": [8, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 64, 65, 66, 67, 68, 70, 71, 72], "exampl": [8, 9, 10, 11, 12, 20, 21, 22, 23, 25, 26, 27, 35, 40, 41, 43, 44, 45, 47, 50, 51, 54, 55, 57, 58, 59, 60, 61, 62, 63, 66, 67, 72, 74], "def": [8, 27, 34, 43, 44, 45, 47, 48, 49, 51, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72], "forty_two": 8, "42": [8, 44, 47, 49, 51, 55, 66], "typevar": [8, 21, 34], "c": [8, 9, 14, 35, 46, 47, 49, 50, 58, 59, 69], "throughout": [9, 63], "being": [9, 27, 34, 45, 48, 51, 56, 57, 65, 68], "model": [9, 10, 11, 14, 16, 26, 27, 29, 34, 38, 39, 44, 46, 53, 54, 58, 59, 60, 61, 68, 69, 71, 73], "wish": [9, 49], "fix": [9, 14, 21, 52, 54, 64, 70, 74], "For": [9, 10, 14, 16, 20, 21, 22, 23, 25, 27, 37, 39, 40, 41, 42, 43, 45, 47, 48, 49, 50, 51, 54, 55, 57, 58, 59, 60, 62, 64, 66, 67, 68, 69, 70, 74], "flexibl": [9, 40, 49, 51, 64, 66], "could": [9, 27, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72, 73], "parameteris": [9, 30, 46], "\u03bc": [9, 16], "\u03b8": 9, "unknown": [9, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 57, 64, 65, 66, 67, 68, 70, 71, 72], "result": [9, 14, 16, 27, 35, 37, 40, 45, 47, 51, 52, 56, 57, 63, 64, 69, 71], "done": [9, 14, 16, 40, 45, 51, 66], "whilst": 9, "learn": [9, 14, 16, 38, 39, 40, 42, 48, 52, 55, 56, 60, 62, 64, 67, 69, 74], "parametr": [9, 52, 67], "first_part": 9, "second_part": 9, "name": [9, 10, 11, 12, 13, 14, 21, 22, 26, 27, 32, 34, 42, 44, 48, 49, 50, 51, 54, 55, 57, 59, 62, 63, 65, 66, 67, 72], "To": [9, 14, 20, 21, 34, 37, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 60, 61, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73], "write": [9, 21, 27, 49, 58, 59, 61, 62, 63], "__call__": [9, 26, 55, 60], "accord": [9, 26, 61], "datum": [9, 16], "heteroskedast": [9, 16, 55, 74], "input_dim": [9, 16], "y_i": [9, 16, 21, 48, 49, 55, 56, 57, 58, 62, 64], "x_i": [9, 21, 23, 25, 32, 48, 49, 55, 56, 57, 58, 64], "b": [9, 10, 14, 19, 22, 27, 35, 44, 45, 46, 49, 51, 54, 67, 68, 69], "mixin": [9, 21], "appropri": [9, 14, 16, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 58, 64, 65, 66, 67, 68, 70, 71, 72], "degre": [9, 14, 55, 60], "output_dim": [9, 14, 21, 22, 42, 45, 51, 65], "static": [9, 21, 27, 29], "compute_pow": 9, "correspond": [9, 14, 16, 27, 34, 46, 48, 49, 55, 57, 67], "power": [9, 74], "rais": [9, 34, 35, 54], "specif": [9, 11, 16, 21, 41, 51, 53, 55, 58, 72, 74], "lexicograph": 9, "order": [9, 14, 16, 49, 50, 52, 65], "length": 9, "neg": [9, 10, 35, 62, 67], "greater": [9, 56], "translat": 9, "term": [9, 16, 21, 22, 62, 73], "sequenc": [9, 10, 11, 12, 13, 14, 16, 19, 20, 21, 22, 27, 31, 34, 36, 49, 57, 59], "function_list": 9, "enabl": [9, 20, 22, 23, 25, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "respect": [9, 21, 34, 46, 48, 49, 56, 64, 69, 70, 71], "label": [9, 16, 42, 45, 47, 49, 50, 54, 55, 56, 57, 58, 64, 65, 71, 72], "extra": [9, 21, 45, 56, 67, 71, 73], "collect": [9, 10, 11, 26, 34, 55, 56, 67], "meanfunction_list": 9, "renam": 9, "compat": [9, 20, 22, 23, 25, 28, 41], "config": [10, 27, 34, 42, 44, 49, 51, 55, 62, 64, 70], "experiment": [10, 52, 65], "kullback_leibl": [10, 54], "likelihood": [10, 20, 21, 22, 23, 25, 26, 27, 29, 34, 38, 40, 42, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 62, 63, 64, 65, 66, 67, 68, 70, 73, 74], "logdens": 10, "monitor": [10, 27, 37, 39, 40, 63], "optim": [10, 14, 16, 21, 25, 34, 40, 42, 43, 44, 45, 46, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 74], "probability_distribut": 10, "type_flag": 10, "recurs": [10, 34, 62], "compos": [10, 48, 58, 60, 62], "creat": [10, 14, 20, 22, 23, 25, 26, 27, 32, 40, 42, 45, 46, 47, 51, 52, 54, 56, 58, 60, 61, 62, 63, 65, 66, 67, 68], "compar": [10, 16, 42, 44, 52, 63, 64, 71, 74], "tf": [10, 21, 25, 27, 29, 34, 35, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72], "includ": [10, 11, 16, 29, 34, 49, 51, 54, 55, 71, 74], "addit": [10, 14, 40, 51, 69], "attribut": [10, 27, 34, 63], "trainable_paramet": [10, 27, 49, 62, 72], "It": [10, 14, 16, 21, 40, 44, 48, 49, 51, 52, 56, 57, 59, 60, 62, 66, 71], "pretti": [10, 49, 56], "within": [10, 15, 54], "ipython": 10, "jupyt": [10, 62], "etc": [10, 58, 62], "guid": [10, 14, 39, 40, 58, 62, 68], "introduct": [10, 14, 16, 39], "tensorflow": [10, 16, 21, 22, 24, 27, 28, 34, 35, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 58, 59, 60, 61, 62, 64, 66, 67, 68, 70, 71, 72, 73, 74], "goe": [10, 47], "why": [10, 60, 62, 67, 68, 74], "thing": [10, 56, 61, 62, 73], "prior_on": [10, 49], "trainabl": [10, 21, 27, 42, 44, 48, 49, 50, 51, 52, 54, 55, 57, 59, 60, 66, 67, 71, 72], "dtype": [10, 24, 35, 42, 44, 45, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 61, 62, 63, 66, 67, 70, 71, 72], "unconstrained_shap": 10, "constrained_shap": 10, "transformedvari": 10, "retain": [10, 24], "constrain": [10, 21, 27, 44, 51, 62, 66, 73], "unconstrain": [10, 27, 44, 48, 51], "often": [10, 19, 40, 49, 56, 58, 59, 61], "challeng": 10, "human": 10, "oper": [10, 14, 32, 35, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 58, 60, 64, 65, 66, 67, 68, 70, 71, 72], "although": [10, 21, 40, 59, 64, 73], "typic": [10, 16, 27, 50, 67], "easier": [10, 49, 58, 59, 67], "optimis": [10, 21, 22, 26, 27, 39, 40, 46, 58, 59, 60, 63], "cannot": [10, 35, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 64, 65, 66, 67, 68, 70, 71, 72], "need": [10, 14, 16, 21, 27, 30, 32, 39, 40, 41, 44, 45, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 69, 72, 73], "natur": [10, 27, 38, 47, 74], "impos": [10, 16], "version": [10, 14, 16, 27, 33, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 58, 64, 65, 66, 67, 68, 70, 71, 72], "declar": [10, 59], "pre": 10, "dynam": [10, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "conveni": [10, 21, 46, 50, 62, 66, 69], "shortcut": 10, "prioron": [10, 49], "assign": [10, 34, 42, 45, 49, 52, 62, 63, 64, 66, 68, 71], "use_lock": 10, "read_valu": 10, "tfp": [10, 27, 34, 44, 48, 49, 59, 62], "4": [10, 14, 22, 35, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72], "like": [10, 16, 22, 28, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 61, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74], "lock": 10, "dure": [10, 16, 20, 22, 23, 25, 34, 44, 51, 52, 58, 59, 60, 63], "someth": [10, 61], "op": [10, 28, 34, 42, 48, 51, 52], "log_prior_dens": [10, 21], "log": [10, 16, 18, 20, 21, 22, 23, 25, 26, 27, 32, 38, 49, 52, 53, 54, 61, 62, 67, 68, 69, 70, 72, 73], "probabl": [10, 16, 21, 27, 30, 41, 57, 62, 67], "densiti": [10, 16, 18, 21, 48, 49, 53, 57, 69, 74], "properti": [10, 11, 12, 14, 27, 30, 51, 52, 54, 57, 62, 66, 67], "els": [10, 44, 54, 65], "directli": [10, 15, 20, 22, 23, 25, 27, 42, 49, 54, 56, 62, 63, 67], "flag": [10, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "iter": [10, 16, 19, 21, 26, 32, 34, 44, 47, 49, 51, 52, 53, 61, 64, 65, 68, 71], "inducing_variable_list": [11, 48, 51], "separ": [11, 14, 46, 48, 55, 57], "design": [11, 40, 47, 51, 74], "interfac": [11, 27, 49, 51, 71], "construct": [11, 14, 21, 22, 34, 38, 46, 48, 49, 51, 53, 54, 55, 64, 68], "requir": [11, 14, 21, 25, 27, 41, 42, 45, 47, 48, 49, 51, 57, 60, 63, 67, 69, 73, 74], "reason": [11, 14, 39, 45, 47, 51, 58, 60, 62, 64], "e": [11, 14, 16, 20, 21, 22, 23, 25, 27, 28, 30, 31, 32, 35, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "advantag": [11, 40, 51, 54, 63, 64], "quit": [11, 26, 59, 66], "py": [11, 47, 48, 51, 72], "defin": [11, 14, 16, 21, 26, 40, 43, 45, 49, 51, 54, 55, 57, 58, 60, 62, 63, 64, 66, 67, 68, 69], "path": [11, 34, 51, 54], "inherit": [11, 14, 16, 21, 32, 51, 66, 67], "independentlatentbas": 11, "up": [11, 19, 21, 35, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 58, 59, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 74], "infer": [11, 14, 16, 38, 48, 58, 67, 68, 74], "sinc": [11, 14, 40, 48, 57, 62, 70], "mani": [11, 21, 25, 40, 45, 58, 62, 67, 69, 70, 74], "acut": 11, "even": [11, 41, 51, 52, 56, 57, 58, 59, 60, 62], "doe": [11, 16, 21, 27, 29, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 63, 64, 65, 66, 67, 68, 70, 71], "definit": [11, 14, 15, 45, 54, 69], "should": [11, 12, 14, 20, 21, 22, 23, 25, 30, 32, 45, 46, 47, 49, 51, 57, 59, 61, 62, 63, 65, 66, 72, 73, 74], "num_induc": [11, 12, 22, 42, 54], "relev": [11, 12, 14, 20, 22, 23, 25, 29, 40, 42, 58, 59, 74], "determin": [11, 12, 14, 21, 42, 51, 57, 58, 60, 67, 69], "z": [11, 12, 21, 22, 25, 31, 44, 47, 48, 49, 50, 51, 59, 65, 67, 69, 72], "inducingpointsbas": 11, "real": [11, 34, 57, 58, 59, 62, 67], "abc": [11, 16, 26, 29, 30], "abstract": [11, 14, 21, 26, 27, 30, 32, 67], "group": [11, 26, 35, 51, 57, 61], "main": [11, 47, 56], "consist": [11, 50, 51, 57, 67], "variou": [11, 21, 51], "becaus": [11, 45, 47, 49, 51, 54, 55, 56, 57, 58, 59, 61, 62, 65, 66, 67, 69, 72, 73], "our": [11, 14, 21, 27, 39, 40, 45, 47, 49, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 73, 74], "eg": 11, "scale": [11, 14, 16, 18, 40, 44, 48, 51, 57, 58, 62], "origin": [11, 14, 24, 34, 40, 43, 44, 53, 54, 59, 64, 71], "propos": [11, 30, 46], "\u00e1": [11, 38], "zaro": [11, 38], "gredilla": [11, 38], "figueira": [11, 38], "vidal": [11, 38], "lazarogfv09": [11, 38], "intend": [11, 62], "without": [11, 14, 19, 20, 22, 23, 25, 27, 29, 39, 51, 54, 60, 73], "custom": [11, 27, 51, 57, 74], "form": [14, 16, 19, 20, 21, 34, 45, 49, 51, 60, 64, 69, 73], "core": [14, 16, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "compon": [14, 16, 34, 54, 67], "encod": [14, 49, 50, 56], "function": [14, 16, 22, 23, 26, 27, 39, 40, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 56, 57, 58, 59, 61, 62, 63, 65, 66, 67, 68, 69, 70, 72, 73, 74], "get": [14, 21, 27, 40, 41, 51, 52, 54, 55, 56, 57, 58, 59, 60, 63, 65, 72, 74], "start": [14, 21, 35, 40, 42, 45, 49, 52, 55, 57, 59, 60, 62, 63, 65, 67, 74], "effect": [14, 40, 44, 49, 56, 58, 69], "choos": [14, 45, 51, 52, 59, 62, 67], "how": [14, 16, 21, 23, 25, 41, 42, 45, 47, 48, 51, 52, 54, 55, 56, 57, 58, 61, 62, 63, 64, 66, 67, 74], "possibl": [14, 21, 27, 40, 51, 53, 54, 56, 59, 62, 73], "shown": [14, 51], "over": [14, 20, 21, 25, 28, 30, 32, 37, 40, 49, 50, 51, 56, 62, 64], "lead": [14, 16, 22, 35, 45, 51, 52, 73], "x1": [14, 44, 45, 57], "x2": [14, 35, 45, 57, 66], "everi": [14, 21, 35, 47, 48, 53, 58, 61, 67, 74], "pair": [14, 27, 35, 55, 64], "s1": [14, 64], "n1": [14, 31], "s2": 14, "n2": [14, 31, 35], "similarli": [14, 52], "contrast": 14, "ident": [14, 22, 44, 51, 62, 67, 69, 71, 73], "lengthscal": [14, 26, 42, 43, 44, 45, 48, 49, 50, 51, 52, 53, 54, 55, 58, 62, 63, 64, 68, 70, 71, 72], "kwarg": [14, 16, 21, 26, 32, 34], "anisotrop": [14, 66], "deriv": [14, 21, 22, 29, 49, 52, 54, 74], "k_d": [14, 66], "self": [14, 21, 26, 27, 32, 34, 54, 55, 60, 62, 65, 66, 67], "pairwis": 14, "\u2113": 14, "x2\u1d40": [14, 35], "last": [14, 15, 32, 45, 62, 63, 68], "axi": [14, 44, 49, 51, 54, 55, 57, 58, 59, 62, 67], "scaled_difference_matrix": 14, "batch2": [14, 35], "weight_vari": 14, "bias_vari": 14, "active_dim": [14, 45, 55, 58, 66], "arc": 14, "famili": [14, 49], "mimic": 14, "neural": [14, 38, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72, 74], "network": [14, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 66, 68, 70, 71, 72, 74], "layer": [14, 34, 64, 65, 67], "perceptron": [14, 67], "mlp": [14, 67], "close": [14, 16, 35, 48, 49, 59, 60, 73], "relat": [14, 56, 58, 71, 74], "kei": [14, 21, 22, 23, 34, 49, 73], "cho": [14, 38], "saul": [14, 38, 48], "cs09": [14, 38], "ard": [14, 42, 50], "alia": [14, 22], "locat": [14, 21, 22, 23, 25, 32, 43, 45, 47, 48, 49, 51, 54, 55, 58, 65, 67], "steep": [14, 43, 58], "along": [14, 32, 40, 47, 58, 59], "1d": [14, 16, 58, 59, 66, 71, 74], "govern": 14, "part": [14, 40, 46, 48, 61, 67, 74], "sigmoid": [14, 43, 44], "\u03c3": [14, 16, 19, 51], "k\u2081": 14, "k\u2082": 14, "deactiv": 14, "around": [14, 27, 57, 60, 67, 74], "found": [14, 16, 20, 21, 22, 34, 35, 68, 71, 72], "lloyd": [14, 38], "llo14": [14, 38], "logist": 14, "x\u2080": 14, "parameter": [14, 27, 43, 45, 49, 52, 73], "list": [14, 26, 27, 31, 32, 34, 35, 40, 45, 51, 55, 58, 60, 62, 63, 64, 67, 71], "ad": [14, 16, 46, 51, 56, 62, 66, 72], "multipli": [14, 58, 60], "composit": 14, "easili": [14, 51, 54, 67, 74], "on_separate_dimens": 14, "check": [14, 16, 41, 49, 62, 74], "act": [14, 45], "disjoint": [14, 64], "subset": [14, 59], "hard": [14, 50, 51, 71], "ass": 14, "overlap": [14, 60, 74], "alwai": [14, 52, 62, 64], "indic": [14, 35, 42, 45, 51, 55, 72], "base_kernel": [14, 44, 62, 65], "image_shap": [14, 44, 65], "patch_shap": [14, 44], "weight": [14, 31, 32, 44, 67], "colour_channel": 14, "plain": [14, 67], "van": [14, 38, 40, 44, 51, 68, 72], "der": [14, 38, 40, 44, 51, 68, 72], "wilk": [14, 38, 40, 44, 51, 68, 72], "et": [14, 21, 23, 27, 38, 40, 47, 48, 49, 67, 69], "al": [14, 21, 23, 27, 38, 40, 47, 48, 49, 67, 69], "vdwrh17": [14, 38], "respons": [14, 61, 67], "individu": [14, 22, 56, 62], "patch": [14, 44], "imag": [14, 61, 65, 74], "sum_p": 14, "th": [14, 45], "get_patch": [14, 44], "extract": 14, "colour": [14, 57], "channel": 14, "rank": [14, 21, 31, 35, 45], "_integers_": 14, "cast": 14, "them": [14, 20, 22, 23, 24, 25, 26, 29, 35, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 58, 60, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 74], "usual": [14, 42, 48, 50, 51, 52, 56, 57, 58, 59, 60, 61, 62, 63, 64, 71, 74], "index": [14, 28, 32, 35, 45, 58], "y": [14, 16, 20, 21, 25, 32, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 63, 64, 66, 67, 69, 70, 71, 72, 73], "kappa": [14, 45], "w\u1d40": 14, "diag": [14, 21, 45, 54, 73], "nb": 14, "symmetri": 14, "element": [14, 21, 22, 24, 26, 29, 34, 35, 45, 73], "local": [14, 44, 68], "avoid": [14, 19, 20, 21, 22, 23, 25, 29, 44, 65, 68, 73], "recommend": [14, 39, 41, 59, 60, 62, 63], "initi": [14, 19, 42, 45, 47, 48, 49, 51, 52, 55, 64, 65, 66, 67, 68, 71], "mcmc": [14, 16, 21, 27, 38, 50, 59, 66, 74], "chain": [14, 44, 48, 50, 74], "random": [14, 35, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 58, 62, 64, 66, 67, 70, 71, 72], "drawn": [14, 21], "sinusoid": [14, 64], "phase": [14, 42], "equat": [14, 43, 45, 46, 47, 49, 50, 51, 54, 56, 57, 58, 60, 62, 66, 67, 74], "\u03c3\u00b2": [14, 21, 34], "2\u03c0d": 14, "per": [14, 21, 29, 31, 46, 47, 51, 58, 64], "\u03c3\u1d62": 14, "\u1d62": 14, "equival": [14, 21, 25, 40, 51], "doubl": 14, "give": [14, 16, 23, 27, 39, 48, 51, 54, 61, 62, 73], "block": [14, 54], "procedur": [14, 45, 63, 64], "place": [14, 48, 49, 70], "simpli": [14, 34, 51, 54, 58, 62, 66, 70, 72], "fallback_independent_latent_": 14, "fallback": 14, "independentinducingvari": [14, 51], "isotrop": [14, 50, 66], "k_r2": [14, 66], "r2": 14, "r\u00b2": 14, "euclidean": 14, "distanc": 14, "wise": [14, 21, 23, 25], "k_r": [14, 66], "scaled_squared_euclid_dist": 14, "\u00b2": [14, 16, 35], "l\u2082": 14, "norm": [14, 44, 51], "basic": [14, 20, 21, 23, 25, 26, 39, 40, 49, 52, 58, 59, 60, 61], "on_separate_dim": 14, "thei": [14, 16, 40, 44, 51, 55, 56, 57, 58, 59, 61, 62, 63, 64, 67, 70, 73], "otherwis": [14, 16, 21, 40, 50, 51], "slice_cov": 14, "turn": [14, 21, 47, 52], "flatten": [14, 31, 49, 50, 53, 61, 65], "d_or_dd": 14, "cx": 14, "\u03c3\u00b2xy": 14, "k_diag": [14, 65], "var": [14, 16, 18, 30, 32, 45, 49, 53, 55, 66, 70], "latent_kernel": 14, "underli": [14, 16, 27, 64], "num_latent_gp": [14, 21, 22, 23, 25, 29, 48, 49, 50, 51, 54, 65], "matern": [14, 45], "differenti": [14, 20, 22, 23, 25, 29, 49, 58, 62], "anywher": 14, "onc": [14, 27, 47, 58, 67], "3r": 14, "twice": [14, 58], "5r": 14, "3r\u00b2": 14, "fill": 14, "until": [14, 21, 34, 61, 64], "reach": [14, 44, 51, 53, 64], "wrap": [14, 21, 27, 29, 47, 49, 51, 58, 61], "canon": 14, "47": [14, 44, 54, 70, 72], "j": [14, 44, 45], "mackai": 14, "bishop": [14, 42, 67], "editor": 14, "machin": [14, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72], "page": [14, 38, 40, 56], "133": 14, "165": 14, "springer": 14, "1998": 14, "map": [14, 16, 27, 32, 34, 42, 47, 48, 49, 57, 62, 65, 73], "u": [14, 21, 22, 27, 40, 42, 46, 49, 51, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 67, 69], "sin": [14, 45, 46, 47, 48, 49, 51, 52, 54, 55, 60, 64, 66, 67, 70], "express": [14, 73], "sin\u00b2": 14, "\u03c0": 14, "\u03b3": 14, "\u2113\u00b2": 14, "factor": [14, 15, 16, 27, 73], "front": 14, "absorb": 14, "hyperparamet": [14, 20, 21, 22, 23, 25, 42, 51, 54, 64, 68, 70, 71, 74], "constructor": [14, 27, 45, 57, 66], "doesn": [14, 24, 67], "offset": 14, "\u1d48": 14, "reducingcombin": 14, "alpha": [14, 18, 21, 29, 45, 46, 47, 48, 49, 51, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 66, 67, 70, 72, 73], "ration": 14, "quadrat": [14, 21, 58, 60], "2\u03b1\u2113\u00b2": 14, "\u03b1": [14, 16], "rel": [14, 34, 49, 60], "small": [14, 16, 39, 40, 45, 47, 49, 51, 52, 55, 56, 57, 59, 61, 64, 69], "fluctuat": 14, "rq": 14, "becom": [14, 51, 56, 62, 73], "priori": [14, 51], "comparison": [14, 54, 59, 68, 71], "purpos": [14, 16, 49, 51, 59], "who": [14, 51], "don": [14, 44, 54, 55, 58, 59, 60, 65], "stand": [14, 42], "automat": [14, 21, 38, 41, 42, 58, 62, 66], "nois": [14, 34, 40, 45, 48, 49, 56, 60, 64, 66, 67, 70, 71, 72, 74], "x_n": [14, 54, 67], "x_m": 14, "\u03b4": 14, "kroneck": 14, "delta": 14, "k_choleski": 15, "kl": [15, 21, 25, 54], "diverg": [15, 21, 25, 38, 54, 58, 69], "3d": [15, 58], "its": [15, 25, 27, 47, 49, 51, 52, 55, 57, 61, 62, 63, 65, 67], "_": [15, 19, 22, 46, 49, 51, 52, 54, 57, 58, 59, 60, 62, 63, 64, 65, 67], "anoth": [16, 43, 50, 52, 58, 59, 62, 63], "under": 16, "assumpt": [16, 21, 44], "made": [16, 49, 51], "continu": [16, 40, 44, 55, 58, 64], "binari": [16, 35, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 58, 64, 65, 66, 67, 68, 70, 71, 72], "count": 16, "better": [16, 44, 52, 57, 58, 59, 60, 63, 69, 72, 73], "introduc": [16, 58, 59, 61, 71], "isn": [16, 52], "alreadi": [16, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "illustr": [16, 47, 49, 59, 64], "regress": [16, 20, 21, 22, 37, 38, 45, 47, 50, 51, 59, 66, 67, 69, 70, 74], "classif": [16, 21, 23, 25, 38, 39, 40, 59, 74], "logp": 16, "conditional_mean": 16, "conditional_vari": 16, "df": [16, 18], "variational_expect": 16, "overriden": 16, "work": [16, 27, 40, 45, 47, 51, 54, 55, 57, 58, 59, 60, 61, 62, 63, 66, 67, 69, 70, 71, 73], "well": [16, 21, 27, 40, 49, 51, 56, 59, 62, 66, 67], "2d": [16, 58, 59, 66], "suitabl": 16, "higher": [16, 45, 49, 52, 58, 59, 72], "invlink": [16, 49, 50, 57], "inv_probit": 16, "scale_lower_bound": 16, "06": [16, 53, 65], "reparameteris": 16, "familiar": [16, 39, 62, 74], "\u03b2": 16, "shape_lower_bound": 16, "invers": [16, 50, 54, 69, 73], "rate": 16, "variance_lower_bound": 16, "believ": 16, "veri": [16, 21, 35, 41, 45, 49, 51, 56, 57, 62, 72], "instabl": 16, "arg": [16, 21, 32, 50, 54, 64], "stochast": [16, 38, 57, 69, 74], "demonstr": [16, 42, 43, 44, 46, 49, 51, 52, 54, 55, 56, 58, 61, 62, 63, 66, 71, 74], "distribution_class": [16, 48], "tensorflow_prob": [16, 44, 48, 49, 59, 62], "scale_transform": [16, 48], "loc": [16, 47, 48, 54, 62, 68], "latent_dim": [16, 21, 35, 42, 48], "observation_dim": 16, "y\u2081": 16, "y\u2096": 16, "margin": [16, 20, 21, 22, 23, 25, 38, 40, 46, 49, 52, 64, 70, 74], "log_prob": [16, 67], "observ": [16, 20, 45, 47, 50, 51, 53, 54, 56, 60, 64, 74], "pdf": [16, 38, 67], "predict_log_dens": [16, 21, 53, 71], "fmu": [16, 32], "predict": [16, 20, 21, 22, 23, 25, 29, 45, 47, 48, 49, 51, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 70, 71, 74], "predict_mean_and_var": 16, "dy": 16, "y\u00b2": 16, "num_class": 16, "driven": 16, "account": [16, 44, 62], "conditional_distribut": 16, "multilat": 16, "bin_edg": [16, 53], "do": [16, 21, 34, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73], "bin": [16, 49], "edg": [16, 44], "switch": [16, 45, 55, 58, 69], "let": [16, 45, 49, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 73], "a\u2080": 16, "a\u2081": 16, "a\u2096": 16, "\u2081": 16, "\u0278": 16, "a\u2082": 16, "cumul": [16, 57], "probit": 16, "chu": [16, 38], "ghahramani": [16, 21, 38, 40], "cg05": [16, 38], "binsiz": 16, "link": [16, 50], "y\u1d62": 16, "f\u1d62": 16, "cox": 16, "doubli": 16, "inhomogen": 16, "intract": [16, 49], "via": [16, 21, 22, 35, 42, 49, 52], "riemann": 16, "gaussianquadratur": 16, "epsilon": [16, 32, 49, 50, 64], "001": [16, 21, 49, 50, 65, 66], "f_1": [16, 45, 48, 50, 51], "f_2": [16, 48], "f_k": 16, "y_1": [16, 45], "y_k": 16, "begin": [16, 21, 23, 25, 43, 45, 46, 47, 49, 50, 51, 55, 56, 57, 58, 64, 66, 67, 69, 73], "arrai": [16, 24, 27, 31, 32, 35, 44, 47, 51, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 71, 72], "ll": [16, 40, 49, 51, 52, 53, 55, 56, 65, 66, 67, 69, 73], "varepsilon": [16, 49, 56], "textrm": [16, 21, 22, 43, 45, 69, 73], "argmax": [16, 49, 50, 65, 67], "end": [16, 21, 23, 25, 43, 45, 46, 47, 49, 50, 51, 55, 56, 57, 58, 66, 67, 68, 69, 72, 73], "help": [16, 19, 40, 49, 55, 57, 58, 60, 62, 63], "scalar": [16, 61], "\u03d5": 16, "those": [16, 21, 46, 49, 55, 57, 58, 61, 62, 64, 74], "after": [16, 27, 44, 47, 49, 52, 62, 63, 65, 68], "univari": 16, "though": [16, 41, 49, 52, 58, 59, 62, 66, 69, 73], "overwritten": 16, "soft": [16, 62], "max": [16, 48, 49, 50, 53, 61, 71], "mont": [16, 32, 50, 74], "carlo": [16, 32, 50, 74], "estim": [16, 20, 21, 22, 23, 25, 45, 70], "tend": 16, "due": [16, 21, 35, 54, 68, 72], "mini": [16, 62], "svgp": [16, 22, 25, 39, 40, 44, 49, 51, 52, 54, 59, 65, 70, 74], "likelihood_list": 16, "mu": [18, 21, 22, 25, 28, 30, 45, 46, 49, 53, 67, 70], "sigma": [18, 21, 22, 25, 43, 46, 55, 56, 57, 58, 66, 67, 69, 73], "want": [18, 19, 20, 21, 22, 23, 25, 26, 27, 29, 35, 44, 46, 49, 51, 52, 55, 56, 57, 58, 63, 64, 71], "lam": 18, "lb": [19, 22, 48], "sigma_sq": [19, 22], "precondition": 19, "q_ff": 19, "\u03c3\u00b2i": [19, 21, 22], "math": [19, 51, 54, 56, 57, 58, 62, 67], "ll\u1d40": 19, "k\u1d64\u1d64": 19, "\u00b2l": 19, "\u00b9k\u1d64\u2093": 19, "aa\u1d40": 19, "l\u1d66l\u1d66\u1d40": 19, "cg_toler": [19, 21, 71], "max_step": 19, "restart_cg_step": [19, 71], "conjug": [19, 21, 38, 49, 74], "gradient": [19, 21, 27, 34, 38, 44, 47, 49, 51, 62, 64, 74], "algorithm": [19, 67, 68], "hesten": 19, "stiefel": 19, "1952": 19, "v_0": 19, "v_1": 19, "v_2": 19, "v_n": 19, "exact": [19, 21, 51, 52, 54, 68, 70, 71], "arithmet": 19, "kv_n": 19, "practic": [19, 21, 38, 42, 52, 58, 59, 67, 71], "v_i": 19, "converg": [19, 44, 45, 49, 51, 60, 61, 64], "quickli": [19, 67], "stop": [19, 44, 51, 52, 53, 62, 71], "satisfi": [19, 32], "r_i": 19, "kv_i": 19, "r\u1d62\u1d40": 19, "\u00b9r": [19, 21, 71], "r\u1d62\u1d40q": 19, "\u00b9r\u1d62": 19, "\u03f5": [19, 21, 71], "backsolv": 19, "psd": 19, "solut": [19, 27, 30, 49, 68, 71], "maximum": [19, 20, 21, 22, 23, 25, 34, 40, 49, 70, 71], "error": [19, 21, 34, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 62, 64, 65, 66, 67, 68, 70, 71, 72], "decis": 19, "boundari": [19, 67], "against": [19, 48, 51, 68], "criteria": [19, 64, 71], "cg": [19, 21, 71], "restart": [19, 21, 63, 68], "step": [19, 21, 26, 27, 45, 47, 49, 52, 62, 64], "reset": [19, 34, 71], "intern": [19, 21, 25, 38, 42, 71], "state": [19, 27, 34, 47, 49, 71], "currect": 19, "build": [19, 21, 40, 49, 50, 51, 53, 62, 65, 67, 74], "kv": [19, 21], "noise_vari": [20, 21, 22, 49, 58, 60, 71], "gpmodel": [20, 22, 23, 25, 46, 57, 59, 60, 61, 62], "internaldatatraininglossmixin": [20, 22, 25, 57], "vanilla": [20, 21, 65], "treat": [20, 21], "mathbf": [20, 21, 25, 46, 49, 50, 51, 54, 69], "mathcal": [20, 21, 23, 25, 45, 46, 48, 49, 51, 54, 55, 56, 57, 58, 67, 69, 73], "sigma_n": [20, 21], "train": [20, 21, 22, 23, 25, 34, 44, 45, 46, 47, 50, 51, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 67, 68, 71, 72, 74], "maximis": [20, 21, 70], "_marginal_": [20, 21], "theta": [20, 21, 23, 25, 67], "usag": [20, 21, 23, 25, 39, 40, 52, 58, 59], "log_marginal_likelihood": [20, 26, 52, 54], "maximum_log_likelihood_object": [20, 22, 23, 25, 67, 70, 72], "maxim": [20, 21, 22, 23, 25, 49, 64], "elbo": [20, 21, 22, 23, 25, 42, 44, 51, 52, 54, 70, 72, 73], "spars": [20, 21, 22, 23, 25, 38, 40, 47, 51, 59, 68, 69, 70, 74], "predict_f": [20, 21, 22, 23, 25, 29, 45, 46, 51, 54, 55, 56, 57, 58, 60, 63, 64, 71], "noisi": [20, 45, 47, 56], "cach": [20, 21, 22, 23, 25, 29, 34, 54, 65, 71, 74], "faster": [20, 22, 23, 25, 29, 52, 56, 73, 74], "subsequ": [20, 22, 23, 25, 65], "precompute_cach": [20, 22, 23, 25, 29, 54], "precomputecachetyp": [20, 22, 23, 25, 54], "three": [20, 22, 23, 25, 27, 42, 46, 49, 51, 55, 62, 63, 66], "quantiti": [20, 22, 23, 25, 29, 73], "graph": [20, 21, 22, 23, 25, 29], "aot": [20, 22, 23, 25, 29], "compil": [20, 21, 22, 23, 25, 27, 29, 34, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 63, 64, 65, 66, 67, 68, 70, 71, 72], "nocach": [20, 22, 23, 25, 29], "immedi": [20, 22, 23, 25, 29, 66], "extran": [20, 22, 23, 25, 29], "you": [20, 21, 22, 23, 25, 27, 29, 35, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 70, 71, 72, 74], "fused_predict_f": [20, 22, 23, 25, 29, 54], "gprposterior": 20, "fuse": [20, 22, 23, 25, 54], "sub": [21, 54, 61], "itself": [21, 24, 29, 40, 60, 66], "overview": [21, 42, 56], "what": [21, 45, 49, 55, 57, 59, 60, 61, 63, 67, 73], "x_data_mean": [21, 42], "x_data_var": [21, 42], "num_inducing_vari": [21, 42], "x_prior_mean": 21, "x_prior_var": 21, "similar": [21, 44, 49, 51, 56, 65, 67, 71, 73], "bayesian": [21, 38, 40, 46, 74], "fit": [21, 25, 42, 45, 53, 57, 58, 59, 60, 63, 68, 70], "training_mixin": 21, "log_posterior_dens": [21, 27, 49], "sensibli": 21, "max_cg_it": [21, 71], "100": [21, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 56, 57, 58, 61, 62, 64, 65, 66, 67, 70, 71, 72], "restart_cg_it": [21, 71], "40": [21, 38, 40, 44, 48, 54, 64, 65, 66, 67, 68, 71], "v_grad_optim": [21, 71], "artemev": [21, 38, 40, 51], "abvdw21": [21, 38], "accuraci": [21, 65], "would": [21, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 64, 65, 66, 67, 68, 70, 71, 72, 73], "increas": [21, 51, 52, 72], "frequent": [21, 26, 46], "auxilari": 21, "track": [21, 27], "jointli": [21, 40, 49, 52, 70], "logdet_term": [21, 22], "common": [21, 22, 60, 62], "low": [21, 38, 40, 45, 49, 59], "tr": [21, 22, 54, 69, 73], "\u03c3\u00b2n": [21, 22], "least": 21, "tight": [21, 70], "appear": [21, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "commontensor": [21, 22], "residu": 21, "agre": 21, "while": [21, 51, 55, 56, 57, 64], "recov": [21, 52, 56, 58, 62], "r\u1d40q": [21, 71], "predict_i": [21, 44, 47, 48, 51, 53, 55, 56, 57, 59, 62, 63, 65, 66, 70, 71, 72], "held": [21, 62], "quad_term": [21, 22], "auxiliari": [21, 71], "2y\u1d40v": 21, "v\u1d40": 21, "y\u1d40k": [21, 71], "\u00b9y": [21, 22, 71], "v\u1d40kv": 21, "aux_vec": [21, 71], "bia": [21, 62, 71], "toler": [21, 71], "loss": [21, 27, 34, 48, 57, 62, 64, 71], "own": [21, 51, 52, 63, 65, 71], "uniform": [21, 52, 55], "api": [21, 27, 40, 57, 58, 60], "closur": [21, 27, 34], "scipi": [21, 42, 44, 45, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 70, 71, 72], "subclass": [21, 46, 51, 66], "disabl": [21, 68, 72], "ownediter": 21, "dataset": [21, 40, 42, 45, 47, 49, 51, 52, 55, 57, 59, 64, 65, 71, 74], "batch_siz": [21, 52, 65], "log_likelihood": [21, 68], "lv": [21, 49], "stateless": 21, "align": [21, 23, 25, 45, 49, 55, 73], "sim": [21, 23, 25, 45, 48, 49, 51, 55, 56, 57, 58], "f_i": [21, 23, 25, 45, 48, 49], "mostli": [21, 63], "These": [21, 41, 46, 51, 56, 58, 67, 74], "push": [21, 56], "obtain": [21, 68, 69, 73], "draw": [21, 43, 49, 57, 58, 66, 67], "predict_f_sampl": [21, 49, 57, 58, 61], "calc_num_latent_gp": 21, "nice": [21, 34, 49, 57, 62], "awar": [21, 58, 62], "bit": [21, 49, 51, 62], "broken": 21, "futur": [21, 48, 51], "slightli": [21, 35, 57], "problemat": [21, 34], "re": [21, 27, 40, 44, 45, 47, 55, 56, 57, 62, 69, 70], "http": [21, 22, 34, 38, 40, 49, 51, 62, 65, 68, 72], "github": [21, 22, 40, 41, 72], "com": [21, 22, 41, 72], "issu": [21, 35, 72], "1343": 21, "calc_num_latent_gps_from_data": 21, "dens": [21, 54, 59, 64, 65], "num_data": [21, 23, 42, 47, 53, 54, 57, 65], "gpr_with_posterior": 21, "sgprbase_deprec": 21, "fitc": [21, 22, 70, 74], "snelson": [21, 38], "sg06": [21, 38], "loos": 21, "gpml": 21, "matlab": 21, "librari": [21, 33, 34, 38, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "obvious": [21, 52, 55], "fitc_log_marginal_likelihood": 21, "minim": [21, 27, 42, 44, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 70, 71, 72], "hensman": [21, 23, 38, 40, 44, 47, 49, 51, 54, 69, 73], "hmfg15": [21, 38, 40], "top": [21, 45, 49, 51, 58, 67, 68, 69, 73], "log_likelihood_lower_bound": 21, "sgpr_with_posterior": 21, "titsia": [21, 22, 38, 40, 42, 69, 70], "tit09": [21, 22, 38, 40], "q_diag": [21, 23, 27, 50, 52, 70], "svgp_with_posterior": 21, "hmg15": [21, 23, 38, 40, 74], "vgp_with_posterior": 21, "idea": [21, 25, 47, 59, 62], "minimis": [21, 25, 62], "aid": [21, 25], "boldsymbol": [21, 25, 51, 73], "opper": [21, 38, 40, 46, 73], "archambeau": [21, 38, 40, 46, 73], "oa09": [21, 38, 40], "off": [21, 44, 47, 58, 62, 67], "adjust": [21, 27], "lambda": [21, 26, 44, 49, 54, 63, 65, 69, 71, 73], "approach": [21, 46, 52, 59, 62, 63], "2nd": [21, 35, 60], "rather": [21, 49, 74], "convex": 21, "caus": [21, 52], "difficulti": [21, 49], "q_alpha": 21, "q_lambda": 21, "e_": [21, 25, 73], "k_": [21, 46, 51, 65, 69, 73], "ff": [21, 69, 73], "closure_kwarg": 21, "gprfitc": [22, 68, 70], "__init__": [22, 34, 54, 55, 62, 65, 67], "upper_bound": [22, 72], "upper": [22, 51, 74], "best": [22, 54, 73], "tighten": [22, 71, 72], "just": [22, 51, 52, 54, 55, 56, 58, 60, 62, 64, 66, 67], "especi": 22, "import": [22, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72], "known": [22, 32, 45, 56, 58], "markvdw": [22, 72], "gp_upper": [22, 72], "tit14": [22, 38], "trace": [22, 47, 49, 52, 54, 68], "aat": 22, "namedtupl": 22, "field": [22, 49], "compute_qu": 22, "jensen": 22, "inequ": 22, "log_det": 22, "gpr": [22, 23, 25, 39, 40, 49, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 66, 68, 70, 71, 72], "y\u1d40": 22, "sgprposterior": 22, "externaldatatraininglossmixin": [23, 57, 67], "vgp": [23, 39, 40, 45, 46, 53, 70, 74], "evid": [23, 42, 52, 70], "baseposterior": [23, 54], "structur": [24, 30, 51, 54, 58], "convert": [24, 27, 28, 49, 53], "keep": [24, 52, 56], "forcefulli": 24, "wrapper": [24, 27, 67], "transpar": 24, "vgpposterior": 25, "new_data": 25, "As": [25, 40, 51, 54, 56, 57, 58, 59, 60, 62, 63, 70, 71, 72, 74], "oppos": 25, "whose": [25, 66], "were": [25, 52, 53, 62], "callback": [26, 27, 61], "execut": [26, 51, 61, 65, 66], "task": [26, 44, 45, 61], "current_step": 26, "keyword": [26, 49], "log_dir": [26, 61, 63], "plotting_funct": 26, "fig_kw": 26, "subplots_kw": 26, "unused_kwarg": 26, "max_siz": 26, "keywords_to_monitor": 26, "left_strip_charact": 26, "sensibl": [26, 40, 52, 56], "tensorboard": 26, "match": [26, 27, 34], "By": [26, 49, 66, 73], "bayesianmodel": [26, 67], "task_group": [26, 61, 63], "period": [26, 49, 60, 61, 62, 63], "model_task": [26, 61], "image_task": [26, 61], "plot_predict": [26, 63, 71], "image_sampl": 26, "lml_task": 26, "lml": [26, 54, 72], "plot": [26, 43, 45, 47, 49, 51, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 70, 71, 72], "slow": [26, 51], "less": [26, 43, 44, 52, 56, 57, 71], "slow_task": 26, "fast": 26, "fast_task": 26, "descend": 26, "bodi": 26, "task_or_task": 26, "frequenc": [26, 54, 61, 71], "natgrad": [27, 52], "gamma": [27, 42, 48, 49, 52], "xi_transform": 27, "optimizerv2": [27, 34], "descent": [27, 62], "Its": 27, "public": [27, 40], "signatur": [27, 32], "var_list": [27, 34, 52, 65], "furthermor": [27, 55], "NOT": [27, 41], "your": [27, 35, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 74], "cite": [27, 51], "salimbeni": [27, 38], "seh18": [27, 38], "get_config": 27, "dictionari": [27, 34, 63], "serializ": 27, "reinstanti": 27, "later": [27, 55, 63], "save": [27, 39, 40, 66], "loss_fn": [27, 48], "triplet": 27, "\u03be": 27, "q_mu1": 27, "q_sqrt1": 27, "q_mu2": 27, "q_sqrt2": 27, "target_log_prob_fn": [27, 49], "helper": [27, 51, 57, 58, 59, 60, 61, 62, 63], "easi": [27, 58, 60, 61, 62, 63, 66, 74], "read": [27, 40, 61, 62, 63, 65, 74], "hmc_helper": [27, 49], "current_st": [27, 49], "hmc": 27, "hamiltonianmontecarlo": [27, 49], "adaptive_hmc": [27, 49], "simplestepsizeadapt": [27, 49], "run_chain_fn": [27, 49], "sample_chain": [27, 49], "num_burnin_step": [27, 49], "hmc_sampl": 27, "parameter_sampl": [27, 49], "convert_to_constrained_valu": [27, 49], "entri": [27, 35, 45, 58], "target": [27, 34, 64, 67], "bfg": [27, 42, 44, 45, 51, 62, 67, 68], "step_callback": [27, 61, 63], "allow_unused_vari": 27, "scipy_kwarg": 27, "pack": 27, "unpack": 27, "side": 27, "flat": [27, 55], "numpi": [27, 34, 39, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 70, 71, 72], "trainable_vari": [27, 42, 44, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72], "solver": [27, 72], "counter": 27, "insid": [27, 34, 52, 66], "speed": [27, 54, 59, 61, 74], "actual": [27, 32, 35, 41, 52, 56, 58, 59, 61, 63], "optimizeresult": 27, "descript": [27, 38, 51], "mode": [27, 67], "meanvarsqrt_to_xi": 27, "varsqrt": 27, "xi1": 27, "xi2": 27, "xi": 27, "naturals_to_xi": 27, "nat1": [27, 28], "nat2": [27, 28], "appli": [27, 34, 35, 45, 49, 51, 62, 67, 69, 70], "\u03b8\u2081": 27, "\u03b8\u2082": 27, "xi_to_meanvarsqrt": 27, "\u03be\u2081": 27, "\u03be\u2082": 27, "meanvarsqrt": 27, "convers": 27, "necessari": [27, 39, 42, 60], "wrt": [27, 32], "eta1": 28, "eta2": 28, "v_sqrt": 28, "s_sqrt": 28, "final": [28, 43, 44, 45, 46, 47, 51, 53, 56, 61, 62, 64, 65, 67, 69, 73], "x_data": [29, 53, 54], "reli": 29, "qinv": [29, 54], "_precomput": [29, 54], "update_cach": [29, 54], "clear": [29, 62, 67], "recent": 29, "axis_dynam": 29, "That": [29, 45, 52, 62], "might": [29, 51, 55, 56, 57, 61, 63, 64, 67, 71, 72, 73], "wrap_alpha_qinv": [29, 54], "m_m_or_l_m_m": 29, "sgpr": [29, 39, 40, 52, 57, 68, 70, 71, 72, 74], "unseen": [29, 64], "_get_posterior_base_cas": 29, "_get_posterior_fully_correlated_mo": 29, "_get_posterior_independent_mo": 29, "_get_posterior_independentlatent_mo_fallback": 29, "_get_posterior_linearcoregionalization_mo_effici": 29, "errorcontext": [29, 30], "markov": [30, 50, 74], "carl": [30, 38], "rasmussen": [30, 38, 44, 68], "x_t": 30, "x_": 30, "n_gh": [31, 32], "dz": 31, "uni": 31, "stddev\u00b2": 31, "dx": [31, 32], "sum_": [31, 32, 67], "stddev": 31, "z_i": 31, "dz_i": 31, "nd": 31, "n_product": 31, "grid": [31, 49, 50, 51, 59], "built": [31, 45, 48, 60, 62, 63], "dim": [31, 32, 35, 67], "n_quad_point": [31, 32], "repeat": [31, 47, 49, 51, 52, 58, 65, 74], "gauss_hermit": 32, "_build_x_w": 32, "logspac": [32, 47], "fun": [32, 45, 53], "exponenti": [32, 42, 48, 58, 62, 64], "formula": 32, "w_i": 32, "elementwis": 32, "moreov": 32, "in_batch": 32, "n_fun": 32, "out_batch": 32, "h": [32, 44], "xn": 32, "wn": 32, "sum_i": 32, "eval_loc": 32, "dxd": 32, "integrand": 32, "xd": 32, "leav": [32, 51], "item": [32, 49, 54], "overal": 32, "determinist": [32, 42, 48, 50, 56, 62], "thereof": 32, "hint": [33, 62], "parameter_or_funct": 34, "doc": [34, 67], "multipledispatch": 34, "yield": [34, 67], "desir": [34, 51], "autograph": 34, "abl": [34, 45, 54, 58, 62, 63], "overwrit": 34, "sole": 34, "simpl": [34, 43, 44, 51, 54, 55, 56, 59, 61, 62, 63, 66, 71, 74], "loop": [34, 46, 47, 51, 61, 64, 68, 71], "dispatch_or_rais": 34, "get_first_occurr": 34, "occurr": 34, "dispatch_it": 34, "logic": [34, 62], "regist": [34, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "inc": 34, "dec": [34, 38], "revers": 34, "_c": [34, 49, 50], "likelihood_vari": 34, "called_method": 34, "assert": [34, 54, 55, 64, 72], "messag": [34, 45, 52, 53], "notimplementederror": [34, 54], "input_modul": 34, "memo": 34, "kera": [34, 61, 64, 65, 67], "copi": [34, 44, 47, 49, 50, 51, 58, 62, 68, 72], "org": [34, 38, 40, 51, 68], "html": [34, 38, 40], "frozen": 34, "submodul": 34, "param": [34, 47, 49, 51, 64], "overrid": [34, 66], "default_positive_minimum": 34, "default_positive_bijector": 34, "fmt": [34, 50, 54, 58, 66, 72], "find": [34, 40, 59, 62], "traverse_compon": 34, "tablefmt": 34, "maxit": [34, 42, 44, 45, 47, 49, 50, 51, 53, 54, 55, 62, 67, 68, 70, 71, 72], "1000": [34, 42, 44, 46, 47, 49, 50, 51, 55, 62, 64, 70, 72], "At": [34, 44, 51, 67, 69], "gradienttap": [34, 52, 64], "adam": [34, 38, 40, 47, 51, 52, 61, 62, 64, 65, 67], "learnt": 34, "acc": [34, 44, 65], "update_cb": 34, "target_typ": 34, "travers": 34, "accumul": 34, "traverseinput": 34, "substract": 35, "a_shap": 35, "b_shape": 35, "num": [35, 44, 49, 64, 67], "perm": 35, "leading_dim": 35, "transpos": [35, 54, 66], "permut": [35, 42, 64, 72], "ellipsi": 35, "mypi": 35, "valid": [35, 62, 67], "view": [35, 40, 61], "1st": 35, "3rd": 35, "0th": 35, "sess": 35, "transposed_ani": 35, "valueerror": [35, 54], "linearli": 35, "reduc": [35, 55], "pca": 35, "imprecis": 35, "lower_bound": 36, "regularli": [37, 63], "readm": 37, "artem": [38, 40, 51], "david": 38, "burt": 38, "tighter": [38, 52], "proceed": [38, 42], "38th": 38, "confer": [38, 42], "362": 38, "372": 38, "2021": 38, "youngmin": 38, "lawrenc": [38, 42, 47], "deep": [38, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "advanc": [38, 39, 42, 44, 45, 47, 57, 58, 67], "22": [38, 44, 47, 49, 51, 52, 55, 57, 58, 62, 68], "2009": [38, 69, 70, 73], "url": [38, 40, 51], "paper": [38, 40, 44, 49, 51, 54, 64, 73], "nip": [38, 49], "cc": [38, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "3628": 38, "wei": 38, "zoubin": [38, 40], "ordin": [38, 74], "journal": [38, 40, 51], "research": [38, 40, 42, 67], "jul": 38, "1019": 38, "1041": 38, "2005": 38, "hfl13": [38, 74], "jame": [38, 40, 42, 47, 51, 69, 73], "nicolo": [38, 47], "fusi": [38, 47], "neil": [38, 42, 47], "big": [38, 47, 55, 59, 67, 69], "arxiv": [38, 40, 47, 51, 64], "preprint": [38, 47, 64], "1309": 38, "6835": 38, "2013": [38, 47, 69], "alexand": [38, 40], "de": [38, 40], "matthew": [38, 40, 69], "maurizio": 38, "filippon": 38, "variatino": 38, "2015": [38, 47, 49, 62, 67], "neurip": 38, "file": [38, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 61, 63, 64, 65, 66, 67, 68, 70, 71, 72], "6b180037abbebea991d8b1232f8a8ca9": 38, "scalabl": [38, 57, 64, 74], "aistat": [38, 48, 69], "miguel": 38, "\u0131": 38, "bal": 38, "inter": [38, 47, 64], "domain": 38, "featur": [38, 39, 51, 65, 66, 67, 74], "law03": [38, 40], "visualis": [38, 40, 60], "high": [38, 42, 45, 49, 51, 57, 59], "2003": [38, 40, 51], "robert": 38, "languag": 38, "nonparametr": 38, "twenti": 38, "eighth": 38, "aaai": 38, "artifici": [38, 42, 47], "intellig": [38, 42, 47, 62], "2014": [38, 47], "dl": 38, "acm": 38, "citat": 38, "cfm": 38, "id": 38, "2893873": 38, "2894066": 38, "mhtg16": [38, 40], "richard": 38, "turner": 38, "On": [38, 41, 56, 69, 74], "kullback": [38, 69], "leibler": [38, 69], "231": 38, "239": 38, "pmlr": [38, 69], "2016": [38, 48, 69, 73], "mvandwilkn": [38, 40], "17": [38, 40, 41, 44, 47, 49, 51, 52, 54, 55, 57, 58, 62, 63, 72], "tom": [38, 40], "nickson": [38, 40], "keisuk": [38, 40], "fujii": [38, 40], "alexi": [38, 40], "boukouvala": [38, 40], "pablo": [38, 40], "le": [38, 40], "\u00f3": 38, "villagr": [38, 40], "flow": [38, 40, 42, 74], "aussian": [38, 40, 51], "ensor": [38, 40], "18": [38, 40, 41, 44, 49, 51, 52, 54, 55, 58, 59, 62, 63, 70, 72], "apr": [38, 40], "2017": [38, 40, 44, 68], "jmlr": [38, 40, 54], "v18": [38, 40], "16": [38, 40, 41, 44, 47, 49, 51, 52, 54, 55, 57, 58, 62, 63, 68, 71, 72], "537": [38, 40], "mat17": [38, 40], "graem": 38, "gari": 38, "phd": [38, 40], "thesi": [38, 40], "univers": [38, 67], "cambridg": 38, "manfr": 38, "cedric": 38, "revisit": [38, 73], "786": 38, "792": 38, "hugh": 38, "stefano": 38, "eleftheriadi": 38, "2018": [38, 54, 67], "edward": 38, "pseudo": 38, "1257": 38, "1264": 38, "mit": 38, "press": 38, "2006": 38, "tl10": [38, 40], "michali": [38, 40, 42], "thirteenth": [38, 42], "844": 38, "851": 38, "workshop": 38, "2010": [38, 42, 67], "567": [38, 69], "574": [38, 69], "determinant": 38, "www2": 38, "aueb": 38, "gr": 38, "mtitsia": 38, "titsiasnipsvar14": 38, "30": [38, 44, 49, 56, 58, 59, 61, 62, 63, 67, 70], "6877": 38, "vandwilkdj": [38, 40], "20": [38, 40, 42, 44, 47, 48, 49, 50, 51, 52, 53, 55, 57, 58, 59, 62, 68, 70, 72], "vincent": [38, 40, 51, 64, 67], "dutordoir": [38, 40, 51, 67], "st": [38, 40, 51], "john": [38, 40, 51], "01115": [38, 40, 51], "2020": [38, 40, 51], "ab": [38, 40, 51, 54], "section": [39, 42, 51, 52, 57, 58, 59, 60, 62, 64, 69, 72, 74], "aim": [39, 53], "knowledg": [39, 73], "gpflow": [39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 68, 69, 70, 71, 72, 73, 74], "medium": 39, "necessarili": [39, 45], "go": [39, 56, 58, 60, 62, 67], "too": [39, 51, 52, 58, 59, 61, 62, 71], "much": [39, 44, 46, 49, 51, 52, 54, 56, 57, 58, 61, 67, 71], "mathemat": [39, 40, 51], "technic": [39, 56, 58, 67, 74], "try": [39, 53, 56, 57, 59, 60, 62, 63, 67], "teach": 39, "theori": [39, 67, 73, 74], "behind": [39, 47], "brief": 39, "articl": [39, 40, 51], "longer": [39, 49, 57], "text": [39, 47, 48, 53, 66, 67], "book": 39, "deeper": [39, 47], "understand": [39, 56, 58, 59, 68], "mayb": 39, "good": [39, 55, 59, 60, 62, 63, 64, 65, 71], "previou": [39, 57, 60, 62, 72], "experi": [39, 44, 49, 62, 64], "knowldeg": 39, "instal": [39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "Their": [39, 40, 58, 60], "load": [39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "kind": [40, 56, 58, 60, 62], "supervis": 40, "inher": 40, "tell": [40, 56, 58, 59], "know": [40, 45, 55, 56, 60, 62, 64, 69], "answer": 40, "limit": [40, 44, 51, 53, 56], "procces": 40, "admittedli": 40, "computation": [40, 47, 54], "intens": 40, "wa": [40, 62, 66], "todai": 40, "primarili": 40, "maintain": 40, "compani": 40, "secondmind": 40, "suggest": [40, 45, 51], "depth": [40, 42, 45, 51, 64, 74], "benchmark": 40, "bibliographi": 40, "slew": 40, "straightforward": [40, 49, 55, 73], "exactli": [40, 44, 49, 51, 62, 63], "class": [40, 42, 44, 45, 46, 48, 49, 50, 54, 55, 57, 58, 59, 60, 61, 65, 66, 67, 70, 72, 73, 74], "gpmc": [40, 49], "sgpmc": [40, 49], "suffici": [40, 52, 56], "discuss": [40, 47, 54, 59, 62, 64, 68, 74], "solidifi": 40, "tabl": [40, 51, 54, 62, 64], "summar": [40, 47], "unifi": [40, 51], "extens": [40, 51, 73], "earli": 40, "greatli": 40, "particular": [40, 45, 51, 58, 60, 72], "crucial": [40, 52], "review": [40, 51], "background": 40, "softwar": [40, 51], "vari": [40, 74], "open": [40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "ticket": [40, 54], "stack": [40, 49, 51, 58, 59], "overflow": 40, "easiest": 40, "touch": [40, 44], "slack": 40, "workspac": 40, "feel": [40, 41, 54, 62], "skill": 40, "contribut": 40, "contributor": 40, "bibtex": 40, "gpflow2017": 40, "author": [40, 51], "o": [40, 51, 54, 55, 59, 72], "titl": [40, 43, 44, 47, 49, 50, 51, 64, 72], "year": [40, 51, 62], "month": 40, "volum": 40, "significantli": [40, 52, 58], "extend": [40, 51, 58, 60, 62], "gpflow2020multioutput": [40, 51], "mrc": 40, "fellowship": 40, "epsrc": 40, "grant": 40, "i036575": 40, "n014162": 40, "word": 41, "unfortun": 41, "happen": [41, 45, 46, 59, 60, 62, 65], "manual": [41, 62], "explicitli": [41, 49, 58], "12": [41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72], "13": [41, 42, 44, 46, 47, 49, 51, 52, 54, 55, 57, 58, 59, 62, 63, 64, 66, 68, 72], "14": [41, 42, 44, 47, 49, 51, 52, 53, 54, 55, 57, 58, 62, 63, 64, 72], "7": [41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72], "15": [41, 44, 47, 48, 49, 51, 52, 54, 55, 57, 58, 60, 62, 63, 67, 72], "8": [41, 42, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 67, 71, 72], "9": [41, 42, 44, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 67, 70, 72], "10": [41, 42, 43, 44, 46, 47, 48, 49, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 70, 71, 72], "second": [41, 45, 55, 62, 66], "mac": 41, "maco": 41, "regular": [41, 63], "pypi": 41, "pip": 41, "notic": [41, 51, 55, 56, 57, 58, 59, 60, 61, 62, 63, 67], "free": [41, 54, 68, 74], "pick": [41, 42, 58, 60, 67], "githib": 41, "git": 41, "clone": 41, "cd": 41, "histori": 41, "show": [42, 44, 45, 47, 48, 49, 50, 51, 52, 54, 55, 62, 63, 64, 66, 70, 71, 72, 73, 74], "unsupervis": [42, 74], "reduct": [42, 74], "matplotlib": [42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 70, 71, 72], "pyplot": [42, 43, 44, 45, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 70, 71, 72], "plt": [42, 43, 44, 45, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 70, 71, 72], "ci_util": [42, 44, 45, 46, 47, 49, 50, 51, 52, 54, 55, 64, 65, 67, 68, 70, 72], "reduce_in_test": [42, 45, 46, 47, 49, 50, 51, 52, 54, 55, 64, 65, 67, 68, 70, 72], "default_float": [42, 44, 54, 64, 70], "set_default_float": [42, 44, 49, 51], "set_default_summary_fmt": [42, 44, 49, 51, 55, 62], "inlin": [42, 43, 45, 47, 49, 50, 51, 52, 53, 54, 55, 64, 66, 67, 68, 70, 71, 72], "2023": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "01": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 57, 64, 65, 66, 67, 68, 70, 71, 72], "27": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 59, 62, 64, 65, 66, 67, 68, 70, 71, 72], "38": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "53": [42, 44, 45, 49, 59, 64], "174108": 42, "platform": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "cpu_feature_guard": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "193": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "oneapi": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "onednn": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "cpu": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "instruct": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "critic": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "avx2": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "avx512f": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "fma": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "rebuild": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "312444": 42, "stream_executor": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "dso_load": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "64": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 59, 64, 65, 66, 67, 68, 70, 71, 72], "39": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 59, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72], "libcudart": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "11": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72], "dlerror": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "No": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 64, 65, 66, 67, 68, 70, 71, 72], "directori": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 61, 64, 65, 66, 67, 68, 70, 71, 72], "312473": 42, "cuda": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "cudart_stub": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "29": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 57, 62, 64, 65, 66, 67, 68, 70, 71, 72], "ignor": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 58, 64, 65, 66, 67, 68, 70, 71, 72], "cudart": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "gpu": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "343746": 42, "cuda_bla": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "2981": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "unabl": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "cubla": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "attempt": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "plugin": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "54": [42, 43, 44, 45, 49, 59], "046731": 42, "libnvinf": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "046801": 42, "libnvinfer_plugin": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "046810": 42, "tf2tensorrt": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "py_util": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "trt": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "dlopen": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "tensorrt": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "nvidia": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "miss": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "mention": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 62, 64, 65, 66, 67, 68, 70, 71, 72], "properli": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "oil": 42, "topograph": 42, "three_phase_oil_flow": 42, "npz": 42, "notat": [42, 51, 69, 73], "convert_to_tensor": [42, 47, 54, 70], "56": [42, 44, 45, 64], "878153": 42, "libcuda": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "878182": 42, "cuda_driv": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "263": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "fail": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "cuinit": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "303": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "878207": 42, "cuda_diagnost": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "156": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "driver": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "host": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "2b767c4360ff": [42, 52, 72], "proc": [42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 64, 65, 66, 67, 68, 70, 71, 72], "878492": 42, "belong": [42, 55, 57], "Not": [42, 62], "afterward": [42, 51], "pt": 42, "x_mean_init": 42, "pca_reduc": 42, "x_var_init": 42, "ones": [42, 45, 48, 49, 54, 58], "randomli": [42, 59], "seed": [42, 43, 44, 45, 48, 50, 51, 52, 53, 54, 59, 64, 66, 67, 70, 72], "reproduc": [42, 43, 44, 47, 50, 53, 55, 64, 66, 67], "se": [42, 58], "manipul": [42, 45, 66, 73], "rbf": [42, 44, 58, 59, 64], "ingredi": 42, "bayesiangplvm": 42, "lt": [42, 44, 45, 47, 48, 49, 51, 53, 56, 57, 61, 62, 63, 68, 71], "unreadvari": [42, 62, 71], "600266525158521": 42, "gt": [42, 45, 47, 48, 49, 51, 53, 56, 57, 61, 62, 63, 64, 68, 71], "next": [42, 47, 52, 54, 62, 64, 65, 67], "opt": [42, 50, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 66, 68, 70, 71], "training_loss": [42, 45, 47, 49, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 71, 72], "inspect": [42, 49, 51], "parametersoftplu": [42, 44, 48, 49, 50, 51, 54, 55, 57, 59, 62, 66, 72], "float640": [42, 44, 48, 49, 50, 51, 54, 55, 57, 59, 66, 72], "91801": 42, "lengthscalesparametersoftplu": [42, 44, 49, 50, 51, 54, 55, 57, 59, 62, 72], "86661": 42, "76001": 42, "varianceparametersoftplu": [42, 49, 54, 55, 57, 59, 62, 66, 72], "00648": 42, "parameterident": [42, 44, 48, 49, 50, 51, 54, 55, 57, 62], "98780e": 42, "04430e": 42, "00": [42, 44, 45, 48, 51, 53, 54, 56, 57, 59, 61, 63, 65], "00041": 42, "00154": 42, "zparameterident": [42, 44, 48, 51, 54, 57, 59, 72], "317670e": 42, "723670e": 42, "visual": 42, "manifold": 42, "x_pca": 42, "gplvm_x_mean": 42, "ax": [42, 43, 49, 57, 58, 59, 60, 61, 62, 63, 66, 67, 68, 70, 71], "subplot": [42, 43, 44, 47, 49, 57, 58, 59, 60, 61, 62, 63, 66, 67, 68, 70, 71], "figsiz": [42, 43, 44, 45, 47, 48, 49, 50, 53, 54, 55, 59, 64, 66, 67, 68, 70, 71, 72], "uniqu": [42, 44, 53], "scatter": [42, 48, 55, 57, 58, 59, 60, 61], "set_titl": [42, 43, 49, 58, 66, 68], "2004": 42, "christoph": [42, 45, 67], "gwilym": 42, "multiphas": 42, "dual": 42, "energi": [42, 68, 74], "densitometri": 42, "nuclear": 42, "instrument": [42, 55], "physic": [42, 60], "acceler": 42, "spectromet": 42, "detector": 42, "equip": 42, "327": 42, "1993": 42, "580": 42, "593": [42, 57], "joseph": 43, "hall": 43, "octob": 43, "2019": [43, 44, 64], "changepoint": [43, 58], "regim": [43, 74], "blend": 43, "smoothli": 43, "k_1": [43, 48], "cdot": [43, 45, 48, 54, 55], "bar": [43, 50, 53], "k_2": [43, 48], "width": [43, 44], "123": [43, 44, 45, 47, 49, 50, 53], "style": [43, 47, 66], "ggplot": [43, 47, 66], "plotkernelsampl": [43, 66], "xmin": [43, 66], "xmax": [43, 66], "xx": [43, 49, 66, 70], "linspac": [43, 45, 46, 47, 48, 49, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 70, 71, 72], "multivariate_norm": [43, 49, 50, 53, 66], "188869": 43, "330078": 43, "330106": 43, "359325": 43, "55": [43, 44, 59], "050716": 43, "050788": 43, "050796": 43, "firstli": [43, 49, 73], "base_k1": 43, "matern32": [43, 45, 49, 50, 53, 54, 58, 60], "base_k2": 43, "57": [43, 44, 49, 56, 59, 61, 63], "811276": 43, "811302": 43, "811321": 43, "adddaa52489b": [43, 53], "811572": 43, "secondli": [43, 49], "window": 43, "abruptli": 43, "50": [43, 44, 45, 47, 51, 52, 58, 59, 64, 71], "juli": 44, "rectangl": 44, "classifi": [44, 49], "tall": 44, "wide": [44, 49, 58, 67], "care": [44, 58, 63, 73], "correctli": [44, 49, 59, 72], "set_train": [44, 47, 48, 49, 50, 52, 54, 58, 59, 62, 64, 70, 72], "is_continuous_integr": 44, "set_default_jitt": [44, 49], "set_se": [44, 47, 48, 49, 50, 52, 58, 64], "num_train_data": 44, "num_test_data": 44, "300": [44, 49, 51, 55, 60, 62, 66], "height": [44, 53], "28": [44, 49, 51, 52, 57, 59, 62], "368135": 44, "515967": 44, "515987": 44, "545648": 44, "02": [44, 45, 47, 51, 53, 54, 57], "265833": 44, "265902": 44, "265910": 44, "affine_scalar_bijector": 44, "scale_bijector": 44, "shift_bijector": 44, "make_rectangl": 44, "arr": 44, "x0": [44, 51], "y0": 44, "y1": [44, 45, 57], "make_random_rectangl": 44, "randint": 44, "make_rectangles_dataset": 44, "img": 44, "rang": [44, 47, 48, 49, 50, 51, 52, 56, 57, 61, 62, 64, 65, 71], "finit": 44, "tri": [44, 59], "rw": 44, "rh": 44, "astyp": [44, 49, 50, 54, 65], "xt": [44, 47, 72], "yt": [44, 47, 72], "test_data": 44, "figur": [44, 45, 47, 48, 49, 50, 53, 54, 55, 61, 64, 70, 72], "imshow": [44, 45, 53], "rbf_m": 44, "bernoulli": [44, 52, 57], "05": [44, 46, 48, 50, 55, 62], "738023": 44, "738051": 44, "738075": 44, "1722214fc508": [44, 54, 64], "738352": 44, "rbf_training_loss_closur": 44, "training_loss_closur": [44, 47, 48, 50, 51, 52, 54, 57, 65, 67, 70, 71], "rbf_elbo": 44, "4e": 44, "9408e": 44, "start_tim": [44, 47], "disp": [44, 51, 72], "nfev": [44, 45, 53], "3f": [44, 63], "THE": [44, 51], "220d": [44, 51], "5152": 44, "94077d": 44, "proj": [44, 51], "77693d": 44, "27056d": 44, "08235d": 44, "10286d": 44, "52642d": 44, "96128d": 44, "52086d": 44, "91601d": 44, "98596d": 44, "90683d": 44, "57667d": 44, "87999d": 44, "48569d": 44, "87526d": 44, "00002d": 44, "85857d": 44, "28576d": 44, "81708d": 44, "04265d": 44, "58595d": 44, "34225d": 44, "47617d": 44, "21923d": 44, "37115d": 44, "98398d": 44, "31593d": 44, "96800d": 44, "23801d": 44, "27642d": 44, "17198d": 44, "71734d": 44, "13083d": 44, "72739d": 44, "09537d": 44, "45487d": 44, "07507d": 44, "04335d": 44, "19": [44, 49, 51, 52, 54, 55, 58, 62, 71, 72], "06242d": 44, "80232d": 44, "04829d": 44, "79481d": 44, "21": [44, 47, 49, 51, 52, 55, 58, 59, 61, 62, 65], "04182d": 44, "66211d": 44, "04028d": 44, "52839d": 44, "23": [44, 46, 49, 51, 52, 55, 58, 62, 66], "03795d": 44, "28437d": 44, "24": [44, 49, 51, 52, 55, 62], "03764d": 44, "87340d": 44, "25": [44, 49, 51, 52, 53, 55, 59, 62, 64], "03741d": 44, "66168d": 44, "26": [44, 49, 51, 52, 59, 62], "03735d": 44, "01438d": 44, "03723d": 44, "97105d": 44, "03721d": 44, "89009d": 44, "03719d": 44, "17457d": 44, "problem": [44, 45, 47, 50, 51, 53, 55, 56, 57, 58, 59, 62, 74], "03716d": 44, "04475d": 44, "31": [44, 46, 59, 62, 67], "80645d": 44, "32": [44, 65], "03714d": 44, "73618d": 44, "03": [44, 45, 46, 51, 53], "33": [44, 63], "05487d": 44, "34": [44, 51, 59, 62, 63, 65, 67, 68], "28429d": 44, "35": [44, 56, 59, 61, 63], "56206d": 44, "36": [44, 51, 59], "80378d": 44, "04": [44, 45, 46, 48, 50], "37": [44, 51, 59], "83350d": 44, "14405d": 44, "42994d": 44, "85343d": 44, "tit": [44, 51], "total": [44, 48, 51, 53, 65, 67], "tnf": [44, 51], "tnint": [44, 51], "segment": [44, 51], "explor": [44, 51, 65], "cauchi": [44, 51], "search": [44, 51], "skip": [44, 51], "nact": [44, 51], "projg": [44, 51], "48": [44, 52, 56, 59, 61, 62, 63, 65], "853d": 44, "037d": 44, "60": [44, 48, 54, 59], "371382131218326": 44, "rel_reduction_of_f_": [44, 45, 51], "_factr": [44, 45, 51], "epsmch": [44, 45, 51], "164": 44, "train_acc": 44, "test_acc": 44, "ntest": 44, "68": [44, 62, 64], "33333333333333": 44, "0371e": 44, "f64": [44, 49], "positive_with_min": 44, "max_abs_1": 44, "conv_k": 44, "identifi": [44, 61, 72], "prevent": [44, 54, 62], "shoot": 44, "crazili": 44, "conv_f": 44, "conv_m": 44, "conv_training_loss_closur": 44, "conv_elbo": 44, "conv": 44, "7271e": 44, "1081": 44, "72706d": 44, "34786d": 44, "06198d": 44, "23134d": 44, "03607d": 44, "56137d": 44, "98680d": 44, "96447d": 44, "93739d": 44, "88465d": 44, "88717d": 44, "27202d": 44, "60134d": 44, "11323d": 44, "51602d": 44, "43289d": 44, "49795d": 44, "75563d": 44, "48808d": 44, "60694d": 44, "104": 44, "48453d": 44, "39257d": 44, "393d": 44, "485d": 44, "845328136876162": 44, "NO": [44, 51, 53], "1082": 44, "53996d": 44, "24919d": 44, "35357d": 44, "23531d": 44, "58264d": 44, "04166d": 44, "58157d": 44, "88887d": 44, "48005d": 44, "63927d": 44, "28536d": 44, "02144d": 44, "04313d": 44, "44685d": 44, "74280d": 44, "92359d": 44, "11481d": 44, "74686d": 44, "06073d": 44, "68864d": 44, "40037d": 44, "60668d": 44, "87412d": 44, "58935d": 44, "41535d": 44, "45651d": 44, "04865d": 44, "13752d": 44, "56939d": 44, "02012d": 44, "86627d": 44, "96655d": 44, "60272d": 44, "94558d": 44, "24031d": 44, "93105d": 44, "25261d": 44, "90992d": 44, "73397d": 44, "87163d": 44, "55953d": 44, "81823d": 44, "54265d": 44, "80343d": 44, "19902d": 44, "79432d": 44, "41609d": 44, "78263d": 44, "44911d": 44, "78000d": 44, "18706d": 44, "77623d": 44, "27247d": 44, "76356d": 44, "23204d": 44, "74130d": 44, "84226d": 44, "72099d": 44, "39793d": 44, "71505d": 44, "87291d": 44, "71225d": 44, "25368d": 44, "70691d": 44, "44551d": 44, "70246d": 44, "99899d": 44, "70165d": 44, "66840d": 44, "69736d": 44, "96735d": 44, "69568d": 44, "38151d": 44, "69408d": 44, "61116d": 44, "69308d": 44, "04302d": 44, "68977d": 44, "50422d": 44, "68704d": 44, "03393d": 44, "41": [44, 46, 52], "68478d": 44, "74728d": 44, "68370d": 44, "68973d": 44, "43": [44, 51, 52, 65, 70, 72], "68312d": 44, "17495d": 44, "44": [44, 52, 59, 62, 70, 72], "68205d": 44, "40366d": 44, "45": [44, 59], "68164d": 44, "93859d": 44, "46": [44, 59], "68066d": 44, "14149d": 44, "68038d": 44, "29234d": 44, "68031d": 44, "60556d": 44, "49": [44, 56, 59, 61, 63, 64, 65], "68025d": 44, "92338d": 44, "68010d": 44, "83827d": 44, "51": [44, 59], "67992d": 44, "75352d": 44, "52": [44, 64, 72], "67965d": 44, "09880d": 44, "67954d": 44, "38053d": 44, "67951d": 44, "82728d": 44, "67943d": 44, "35894d": 44, "67915d": 44, "36174d": 44, "67888d": 44, "44453d": 44, "58": [44, 47, 59], "67867d": 44, "69400d": 44, "59": [44, 47, 51, 54], "67852d": 44, "49436d": 44, "67849d": 44, "30110d": 44, "61": [44, 54, 59, 64], "67838d": 44, "45478d": 44, "62": [44, 59, 62, 72], "67818d": 44, "66751d": 44, "63": [44, 59], "67784d": 44, "01109d": 44, "67780d": 44, "20388d": 44, "65": [44, 59], "67748d": 44, "05237d": 44, "66": [44, 49, 59], "67725d": 44, "53573d": 44, "67": [44, 64], "67716d": 44, "91392d": 44, "67709d": 44, "11336d": 44, "69": [44, 64], "67707d": 44, "81715d": 44, "70": [44, 59, 64], "67699d": 44, "71523d": 44, "71": [44, 59], "67687d": 44, "84486d": 44, "72": [44, 64], "67676d": 44, "15235d": 44, "73": [44, 52, 59], "67667d": 44, "34509d": 44, "74": 44, "67662d": 44, "75": [44, 47, 49, 59], "67653d": 44, "22312d": 44, "76": [44, 59, 62], "67642d": 44, "35684d": 44, "77": [44, 59, 65], "67634d": 44, "13194d": 44, "78": [44, 59], "67632d": 44, "30113d": 44, "79": [44, 49], "67626d": 44, "95710d": 44, "80": [44, 48, 56, 59, 61, 63], "67625d": 44, "88159d": 44, "81": [44, 59], "67616d": 44, "65936d": 44, "82": [44, 52, 56, 57, 59, 61, 63], "67614d": 44, "95283d": 44, "83": [44, 59], "67611d": 44, "94345d": 44, "84": [44, 59], "67606d": 44, "65529d": 44, "85": [44, 59], "67587d": 44, "14022d": 44, "86": 44, "67585d": 44, "94482d": 44, "87": [44, 59], "67577d": 44, "20143d": 44, "88": 44, "67576d": [44, 51], "06103d": 44, "89": [44, 64], "67569d": 44, "29646d": 44, "90": [44, 59], "67567d": 44, "60409d": [44, 51], "91": [44, 56, 59, 61, 63], "67563d": 44, "82486d": 44, "92": 44, "67559d": 44, "57009d": 44, "93": [44, 57, 59], "67557d": 44, "98616d": 44, "94": [44, 72], "67553d": 44, "90014d": 44, "95": [44, 49, 56, 62], "67549d": 44, "35560d": 44, "96": [44, 55, 56, 57, 58, 59, 60, 62, 63], "67545d": 44, "33563d": 44, "97": [44, 65], "67542d": 44, "03929d": 44, "98": [44, 59], "67540d": 44, "02593d": 44, "99": [44, 57], "67536d": 44, "68131d": 44, "67533d": 44, "69556d": 44, "114": [44, 54], "696d": 44, "675d": 44, "753331958808452": 44, "6753e": 44, "06365d": 44, "86139d": 44, "67532d": 44, "55833d": 44, "67531d": 44, "20632d": 44, "67530d": 44, "62645d": 44, "67527d": 44, "66727d": 44, "67524d": 44, "89510d": 44, "42522d": 44, "67522d": 44, "23353d": 44, "71282d": 44, "67521d": 44, "07164d": 44, "67519d": 44, "64874d": 44, "67517d": 44, "46018d": 44, "67515d": 44, "57820d": 44, "67514d": 44, "00336d": 44, "67513d": 44, "49494d": 44, "67512d": 44, "87451d": 44, "67510d": 44, "21678d": 44, "67507d": 44, "64757d": 44, "67505d": 44, "41873d": 44, "67504d": 44, "41570d": 44, "67503d": 44, "18225d": 44, "67502d": 44, "63585d": 44, "67501d": 44, "14117d": 44, "27715d": 44, "67499d": 44, "32219d": 44, "55878d": 44, "67497d": 44, "21886d": 44, "67496d": 44, "57636d": 44, "40242d": 44, "94792d": 44, "02854d": 44, "42601d": 44, "67495d": 44, "01797d": 44, "46539d": 44, "81388d": 44, "67494d": 44, "67147d": 44, "56626d": 44, "03325d": 44, "37251d": 44, "60650d": 44, "48639d": 44, "04997d": 44, "67493d": 44, "52702d": 44, "24150d": 44, "67492d": 44, "77971d": 44, "01161d": 44, "04371d": 44, "91164d": 44, "42234d": 44, "35007d": 44, "67491d": 44, "08262d": 44, "67490d": 44, "03729d": 44, "75642d": 44, "25489d": 44, "67489d": 44, "03603d": 44, "15719d": 44, "67488d": 44, "15185d": 44, "94135d": 44, "67487d": 44, "20700d": 44, "67485d": 44, "75814d": 44, "67484d": 44, "29942d": 44, "67483d": 44, "17542d": 44, "67482d": 44, "50787d": 44, "67481d": 44, "88446d": 44, "67477d": 44, "76959d": 44, "67475d": 44, "17387d": 44, "67473d": 44, "14275d": 44, "67472d": 44, "79496d": 44, "67471d": 44, "84332d": 44, "67470d": 44, "70335d": 44, "67467d": 44, "72707d": 44, "67466d": 44, "05473d": 44, "67465d": 44, "82233d": 44, "67463d": 44, "06469d": 44, "67461d": 44, "38709d": 44, "67456d": 44, "56594d": 44, "67451d": 44, "11022d": 44, "67450d": 44, "90648d": 44, "67444d": 44, "48865d": 44, "67443d": 44, "33044d": 44, "67442d": 44, "89315d": 44, "67440d": 44, "31826d": 44, "67435d": 44, "62591d": 44, "67428d": 44, "75926d": 44, "67423d": 44, "89902d": 44, "67418d": 44, "96004d": 44, "67414d": 44, "27813d": 44, "67407d": 44, "62477d": 44, "67399d": 44, "14672d": 44, "67392d": 44, "17359d": 44, "67390d": 44, "54427d": 44, "67388d": 44, "84208d": 44, "67387d": 44, "62589d": 44, "67385d": 44, "58118d": 44, "67383d": 44, "18687d": 44, "67382d": 44, "74468d": 44, "67380d": 44, "18287d": 44, "67375d": 44, "26550d": 44, "67363d": 44, "57415d": 44, "111": [44, 54], "574d": 44, "674d": 44, "736287663325719": 44, "6736e": 44, "1226": 44, "15890d": 44, "66593d": 44, "23447d": 44, "59601d": 44, "31911d": 44, "38946d": 44, "04322d": 44, "21797d": 44, "72697d": 44, "18210d": 44, "20448d": 44, "15484d": 44, "52929d": 44, "09121d": 44, "21088d": 44, "96627d": 44, "42157d": 44, "88499d": 44, "41832d": 44, "82255d": 44, "55848d": 44, "79084d": 44, "36303d": 44, "78952d": 44, "36235d": 44, "78289d": 44, "01208d": 44, "78061d": 44, "28140d": 44, "77800d": 44, "28107d": 44, "77399d": 44, "38815d": 44, "77171d": 44, "45748d": 44, "77002d": 44, "60301d": 44, "76745d": 44, "24458d": 44, "76264d": 44, "78105d": 44, "75997d": 44, "23336d": 44, "75696d": 44, "70236d": 44, "75675d": 44, "71359d": 44, "75597d": 44, "01336d": 44, "75532d": 44, "75464d": 44, "75458d": 44, "28402d": 44, "75438d": 44, "03329d": 44, "75401d": 44, "09040d": 44, "75372d": 44, "97689d": 44, "75283d": 44, "93077d": 44, "75172d": 44, "99012d": 44, "75019d": 44, "42903d": 44, "74767d": 44, "11521d": 44, "74668d": 44, "55860d": 44, "74598d": 44, "89704d": 44, "74518d": 44, "30937d": 44, "74498d": 44, "79222d": 44, "74485d": 44, "79688d": 44, "74466d": 44, "39104d": 44, "74434d": 44, "27033d": 44, "74411d": 44, "58730d": 44, "74314d": 44, "00359d": 44, "74250d": 44, "18368d": 44, "74148d": 44, "05909d": 44, "74124d": 44, "85410d": 44, "74061d": 44, "72040d": 44, "74016d": 44, "82946d": 44, "73960d": 44, "56201d": 44, "73897d": 44, "66155d": 44, "73790d": 44, "06765d": 44, "73687d": 44, "68134d": 44, "73640d": 44, "59985d": 44, "73575d": 44, "21741d": 44, "73540d": 44, "82679d": 44, "73476d": 44, "50497d": 44, "73343d": 44, "32714d": 44, "73297d": 44, "87886d": 44, "73082d": 44, "35077d": 44, "72966d": 44, "61551d": 44, "72792d": 44, "95599d": 44, "72629d": 44, "38795d": 44, "72463d": 44, "98290d": 44, "72448d": 44, "30648d": 44, "72353d": 44, "29832d": 44, "72286d": 44, "86780d": 44, "72173d": 44, "29611d": 44, "72027d": 44, "74830d": 44, "72005d": 44, "23360d": 44, "71839d": [44, 51], "81289d": 44, "71796d": 44, "93730d": 44, "71718d": 44, "78583d": 44, "71642d": 44, "34851d": 44, "71543d": 44, "65164d": 44, "71522d": 44, "92592d": 44, "71470d": 44, "37492d": 44, "71289d": 44, "56450d": 44, "71213d": 44, "03391d": 44, "71175d": 44, "60273d": 44, "71117d": 44, "91271d": 44, "71087d": 44, "43123d": 44, "71059d": 44, "98718d": 44, "71032d": 44, "70994d": 44, "71007d": 44, "22893d": 44, "70956d": 44, "84796d": 44, "70912d": 44, "92854d": 44, "70883d": 44, "66597d": 44, "70864d": 44, "27289d": 44, "70852d": 44, "05707d": 44, "70840d": 44, "16601d": 44, "70824d": 44, "37873d": 44, "70809d": 44, "89050d": 44, "70803d": 44, "73995d": 44, "70786d": 44, "65289d": 44, "70773d": 44, "79195d": 44, "70754d": 44, "50309d": 44, "70727d": 44, "16541d": 44, "70713d": 44, "70686d": 44, "99336d": 44, "70672d": 44, "34938d": 44, "70665d": 44, "01578d": 44, "121": [44, 62], "016d": 44, "707d": 44, "066503593133774": 44, "66666666666667": 44, "7067e": 44, "float643": [44, 49], "56655": 44, "float642": [44, 51, 66], "75129": 44, "196": [44, 57], "78240e": 44, "parameterfilltriangular": [44, 48, 51, 54, 57], "4475e": 44, "0000e": [44, 48, 51, 57], "parametersigmoid": [44, 49, 50], "float6499": 44, "98292": 44, "64773": 44, "144": [44, 52], "11865": 44, "30752": 44, "43216": 44, "00999": 44, "2640e": 44, "strong": 44, "mathbb": [45, 51, 73], "rightarrow": [45, 51], "x_1": [45, 56], "dot": [45, 48, 49, 50, 51, 54, 60, 67], "x_p": 45, "f_p": [45, 51], "f_j": 45, "prime": 45, "intrins": 45, "icm": 45, "bonilla": 45, "william": 45, "2008": 45, "previous": [45, 51, 72], "augment": 45, "essenti": 45, "switchedlikelihood": 45, "rcparam": [45, 53, 70, 72], "247191": 45, "382647": 45, "382668": 45, "412502": 45, "088070": 45, "088138": 45, "088146": 45, "6x": 45, "epsilon_1": 45, "qquad": 45, "009": 45, "y_2": 45, "epsilon_2": 45, "heavi": [45, 62], "tail": [45, 54, 57], "One": [45, 47, 49, 50, 64], "rand": [45, 47, 49, 50, 51, 53, 54, 66, 70], "randn": [45, 47, 49, 51, 54, 64, 66, 67, 70], "y2": [45, 57], "mew": [45, 47, 49, 53, 56, 57, 59, 62, 63, 66, 70], "x_augment": 45, "vstack": [45, 49, 53, 72], "hstack": [45, 51, 55], "zeros_lik": [45, 47, 54, 57, 59, 71, 72], "ones_lik": [45, 54, 57], "y_augment": 45, "product": 45, "tutori": [45, 57], "coreg": 45, "kern": [45, 53], "998793": 45, "998823": 45, "998846": 45, "2da0ea17d0b1": [45, 65], "999113": 45, "saddl": 45, "henc": [45, 47, 49, 58, 64], "lik": 45, "now": [45, 47, 49, 51, 52, 53, 54, 55, 56, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72], "10000": [45, 47], "success": [45, 53], "statu": [45, 53], "225": 45, "66181154535906": 45, "948e": 45, "215e": 45, "389e": 45, "835e": 45, "nit": [45, 53], "1378": 45, "jac": [45, 53], "367e": 45, "451e": 45, "257e": 45, "610e": 45, "1519": 45, "njev": [45, 53], "hess_inv": [45, 53], "11483x11483": 45, "lbfgsinvhessproduct": [45, 53], "plot_gp": [45, 54], "color": [45, 47, 48, 49, 50, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 66, 68, 69, 70], "lw": [45, 47, 49, 53, 57, 58, 59, 60, 61, 62, 63, 66, 70], "fill_between": [45, 47, 48, 49, 51, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 66, 70, 72], "xtest": [45, 49, 53, 68, 70], "line": [45, 47, 49, 50, 51, 53, 55, 58, 60, 62, 66], "get_color": [45, 47, 49, 53, 54, 57, 58, 59, 60, 62, 63, 66], "legend": [45, 47, 49, 50, 54, 56, 58, 64, 71, 72], "blue": [45, 59, 64, 67, 71], "everywher": 45, "orang": 45, "job": 45, "recognis": [45, 66, 73], "curv": [45, 64], "truth": [45, 47, 64], "output_covari": 45, "85387406": 45, "65422127": 45, "44798141": 45, "edwin": 45, "kian": 45, "chai": 45, "scratch": 46, "interleav": [46, 52], "simplifi": [46, 57, 58, 73], "upon": 46, "reus": [46, 51, 59, 62, 65], "capabl": 46, "togeth": [46, 47, 51, 58, 68], "nm": [46, 59], "mm": 46, "2i": 46, "nn": [46, 51, 67], "mn": 46, "nu": [46, 58], "uu": [46, 51, 54, 69], "un": [46, 62, 63], "l_b": 46, "n_data": [46, 55], "inducing_point": [46, 59], "529334": 46, "696195": 46, "696228": 46, "736009": 46, "481825": 46, "481928": 46, "481940": 46, "abstractposterior": 46, "07": [46, 56, 59, 61, 63, 64, 68], "986706": 46, "986738": 46, "986762": 46, "a2ff214cf20c": [46, 66], "987094": 46, "timeit": [46, 47], "189": 46, "std": [46, 47, 49, 53, 55, 64, 67], "dev": [46, 47, 67], "retriev": [46, 65], "138": [46, 52], "likewis": 46, "243": [46, 56, 59, 61, 63], "again": [46, 52, 55, 58, 61, 62, 63, 70], "106": 46, "394": 46, "152": 46, "art": 47, "overcom": 47, "itertool": 47, "rng": [47, 49, 55, 59], "randomst": [47, 49], "892777": 47, "032108": 47, "032136": 47, "061315": 47, "755703": 47, "755776": 47, "755784": 47, "000": [47, 64], "pi": [47, 48, 50, 54, 67, 69], "frac": [47, 58], "noiseless": 47, "smaller": [47, 52, 56, 57, 59, 62], "thought": 47, "larger": [47, 56, 67], "776181": 47, "776208": 47, "776231": 47, "4489dac956ca": [47, 67], "776486": 47, "showcas": 47, "whole": [47, 61], "tensor_data": 47, "17730": 47, "676725310346": 47, "minibatch_s": 47, "train_dataset": 47, "from_tensor_slic": [47, 52], "shuffl": [47, 52, 65, 67], "train_it": 47, "ground_truth": 47, "529": 47, "\u00b5": 47, "unbias": 47, "histogram": 47, "ground": [47, 64], "eval": 47, "islic": 47, "hist": [47, 49], "axvlin": 47, "discrep": [47, 59, 64, 72], "802624793072027": 47, "decreas": [47, 72], "cheaper": 47, "fewer": 47, "minibatch_proport": 47, "mbp": 47, "batchsiz": 47, "append": [47, 49, 53, 55, 64, 67, 72], "ax1": [47, 62], "ax2": [47, 62], "set_xlabel": [47, 49, 71], "proport": 47, "set_ylabel": [47, 49, 71], "kx": [47, 49, 53, 56, 57, 59, 62, 63, 66, 70], "px": [47, 51, 72], "pyv": [47, 51, 72], "col": [47, 53], "kingma": 47, "ba": 47, "run_adam": [47, 64], "action": [47, 64], "logf": [47, 64], "optimization_step": [47, 61, 64, 65], "20000": [47, 68], "arang": [47, 49, 50, 53, 54, 72], "xlabel": [47, 49, 50, 51, 67, 71, 72], "ylabel": [47, 49, 50, 51, 53, 67, 71, 72], "sever": [47, 51, 64, 68], "expand": [47, 69, 73], "diederik": 47, "jimmi": 47, "1412": 47, "6980": 47, "wherea": [48, 60, 64, 68], "captur": [48, 59, 62, 64], "connect": [48, 57], "gpf": [48, 51], "777086": 48, "920715": 48, "920734": 48, "950306": 48, "694900": 48, "694973": 48, "694982": 48, "substitut": [48, 69, 73], "1001": 48, "uniformli": 48, "interv": [48, 54, 55, 56, 57, 64], "quad": [48, 56, 57, 58], "f1": 48, "f2": 48, "shade": [48, 55], "area": [48, 55, 60], "plot_distribut": [48, 55], "squeez": [48, 49, 54, 55, 57, 61, 64, 71], "ub": 48, "silver": [48, 55], "black": [48, 55, 58, 59, 60], "grai": [48, 55], "heteroskedastictfpcondit": 48, "842382": 48, "842410": 48, "842431": 48, "c8602a4092f7": [48, 68], "842694": 48, "k1": [48, 66], "k2": [48, 66], "u_1": 48, "u_2": 48, "z_1": 48, "z_2": 48, "2m": 48, "min": [48, 49, 53, 61, 66, 71], "u1": 48, "z1": 48, "u2": 48, "z2": 48, "0x7fbf4edd70d0": 48, "float641": [48, 49, 50, 51, 54, 57, 59], "variational_var": 48, "natgrad_opt": [48, 52], "naturalgradi": [48, 52], "adam_var": 48, "adam_opt": [48, 52, 65], "optimisation_step": 48, "epoch": [48, 64], "log_freq": 48, "4f": [48, 65], "ymean": 48, "yvar": 48, "ystd": 48, "tmp": [48, 51], "max_venv": [48, 51], "lib": [48, 51], "python3": [48, 51], "site": [48, 51], "deprec": [48, 51], "629": [48, 51], "map_fn_v2": [48, 51], "map_fn": [48, 51, 65], "remov": [48, 51], "fn_output_signatur": [48, 51], "1471": 48, "8678": 48, "1452": 48, "4426": 48, "1450": [48, 51], "7381": 48, "0566": 48, "1449": 48, "6072": 48, "83707": 48, "18477": 48, "13101": 48, "05985": 48, "11665": 48, "26969": 48, "38261": 48, "07056": 48, "6401e": 48, "hamiltonian": [49, 74], "multiclass_classif": [49, 50], "plot_from_sampl": 49, "tfd": [49, 65], "plai": 49, "to_default_float": [49, 54, 62, 65], "930623": 49, "060247": 49, "060275": 49, "089112": 49, "756283": 49, "756350": 49, "756358": 49, "tau": 49, "varepsilon_i": [49, 56, 57, 58], "treatment": [49, 50], "direct": [49, 52], "synthetic_data": 49, "toi": [49, 54, 67], "propto": [49, 50], "matern52": [49, 52, 58], "linear": [49, 51, 58, 60, 62, 65, 67], "673110": 49, "673140": 49, "673162": 49, "28ad2f0300e8": 49, "673426": 49, "optimum": [49, 68], "460240793869067": 49, "thirdli": 49, "79274": 49, "37839": 49, "85356": 49, "07945": 49, "shiftgamma": 49, "01652": 49, "samplinghelp": 49, "num_leapfrog_step": 49, "step_siz": 49, "num_adaptation_step": 49, "target_accept_prob": 49, "adaptation_r": 49, "num_result": 49, "trace_fn": 49, "pkr": 49, "inner_result": 49, "is_accept": 49, "param_to_nam": 49, "parameter_dict": [49, 63, 72], "plot_sampl": 49, "y_axis_label": 49, "val": 49, "zip": [49, 64, 67], "bbox_to_anchor": 49, "marginal_sampl": 49, "fig": [49, 53, 61, 67, 71], "len": [49, 51, 54, 64, 67, 68, 72], "constrained_layout": 49, "suptitl": 49, "sampler": 49, "remain": 49, "seriou": 49, "analysi": 49, "certainli": 49, "plot_joint_margin": 49, "name_to_index": 49, "signal_vari": 49, "Then": [49, 56], "var_sampl": 49, "c0": [49, 56, 57, 61, 70], "xlim": [49, 55], "ylim": 49, "modal": [49, 67], "explain": [49, 58, 60, 62, 67, 72, 74], "long": [49, 62, 65, 72], "signal": [49, 55, 57], "shorter": 49, "f_c": [49, 50], "formul": 49, "u_c": 49, "ey": [49, 50, 51, 64], "hot": [49, 50], "y_hot": [49, 50], "argsort": [49, 50], "joint": [49, 50], "beta": [49, 50], "37454": 49, "5875": 49, "variation": 49, "7654902747724": 49, "burn": 49, "500": [49, 51, 62, 64], "constrained_sampl": 49, "report": [49, 64, 67], "thin": 49, "displai": 49, "param_nam": 49, "sometim": [49, 56, 58, 72], "glm": 49, "literatur": 49, "rotat": [49, 69, 70], "adopt": 49, "ve": [49, 57, 58, 66], "applic": 49, "deal": [49, 67, 74], "arbitrari": [49, 57, 61], "posteriori": 49, "3000": 49, "600": [49, 51, 62], "f_sampl": 49, "rate_sampl": 49, "percentil": 49, "sharex": [49, 66, 70, 71], "tight_layout": 49, "prior_distribut": 49, "reflect": [49, 62], "set_default_positive_bijector": 49, "set_default_positive_minimum": 49, "meanf": 49, "run_chain_fn_unconstrain": 49, "cal": 50, "discret": [50, 53], "bigger": 50, "fashion": 50, "pi_1": 50, "pi_c": 50, "sum_c": 50, "prod_c": 50, "softmax": [50, 67], "robust": [50, 59], "mbox": 50, "max_c": 50, "filterwarn": 50, "deprecationwarn": 50, "plot_posterior_predict": 50, "526581": 50, "708254": 50, "708282": 50, "746698": 50, "472978": 50, "473050": 50, "473058": 50, "jitter_ey": 50, "kernel_s": [50, 65], "08": [50, 59, 64, 66, 68], "582896": 50, "582949": 50, "582973": 50, "1da88dc6cf3b": [50, 70], "583289": 50, "robustmax": 50, "54881": 50, "opt_log": 50, "float64136384": 50, "63633": 50, "17436": 50, "23227": 50, "61397": 50, "3817": 50, "08248": 50, "07942": 50, "12069": 50, "modular": 51, "exis": 51, "grip": 51, "daunt": 51, "accompani": 51, "level": [51, 67], "choic": [51, 52, 59, 62, 71], "reader": 51, "hope": 51, "adapt": [51, 64], "newcommand": 51, "rr": 51, "ee": 51, "valpha": 51, "vf": 51, "vg": 51, "vw": 51, "vi": 51, "vz": 51, "vu": 51, "vx": 51, "vy": 51, "coregion": [51, 74], "subopt": 51, "denot": 51, "g_": 51, "g_l": 51, "k_l": 51, "f_": 51, "2000": 51, "282180": 51, "425220": 51, "425243": 51, "455756": 51, "166983": 51, "167053": 51, "167062": 51, "generate_data": [51, 53, 55, 64], "matmul": [51, 54, 64, 67], "zinit": [51, 72], "plot_model": [51, 57, 59, 60, 72], "ndim": [51, 54], "gca": 51, "set_prop_cycl": 51, "bot": 51, "iv": [51, 59, 71], "977045": 51, "977070": 51, "977091": 51, "56de5f5f9170": [51, 71], "977340": 51, "optimize_model_with_scipi": 51, "424": 51, "26251d": 51, "79322d": 51, "60046d": 51, "23880d": 51, "24335d": 51, "64482d": 51, "150": 51, "47594d": 51, "30324d": 51, "200": [51, 57, 59, 62, 63, 64, 67, 71], "09409d": 51, "79887d": 51, "250": 51, "85812d": 51, "69594d": 51, "68431d": 51, "00237d": 51, "350": 51, "56696d": 51, "56927d": 51, "400": [51, 62], "46591d": 51, "61969d": 51, "450": 51, "37202d": 51, "01165d": 51, "30875d": 51, "36795d": 51, "550": 51, "27808d": 51, "06301d": 51, "26544d": 51, "51395d": 51, "650": [51, 57], "25500d": 51, "33529d": 51, "700": [51, 62], "24944d": 51, "56079d": 51, "750": 51, "24630d": 51, "78334d": 51, "800": [51, 62], "24463d": 51, "26999d": 51, "850": 51, "24381d": 51, "16215d": 51, "900": [51, 62], "11149d": 51, "950": 51, "24295d": 51, "49405d": 51, "24265d": 51, "33535d": 51, "1050": 51, "24249d": 51, "05105d": 51, "1100": [51, 62], "24240d": 51, "28053d": 51, "1150": 51, "24235d": 51, "1200": [51, 62], "24230d": 51, "49874d": 51, "1250": 51, "24225d": 51, "82735d": 51, "1300": [51, 62], "24221d": 51, "34652d": 51, "1350": 51, "24218d": 51, "27220d": 51, "1400": [51, 62], "24214d": 51, "21356d": 51, "24211d": 51, "22174d": 51, "1500": [51, 62, 67], "24208d": 51, "25751d": 51, "1550": 51, "24205d": 51, "64768d": 51, "1600": [51, 62], "55818d": 51, "1650": [51, 52], "24204d": 51, "40386d": 51, "1700": [51, 62], "07473d": 51, "1813": 51, "075d": 51, "242d": 51, "420424440816490": 51, "92725": 51, "79819": 51, "2139": 51, "03966": 51, "83959": 51, "90097": 51, "69851": 51, "4739": 51, "7120e": 51, "fn": [51, 62, 63], "7981918482945918": 51, "kern_list": 51, "430": 51, "94337d": 51, "19142d": 51, "66814d": 51, "26283d": 51, "00999d": 51, "15028d": 51, "97328d": 51, "95679d": 51, "64796d": 51, "71966d": 51, "44078d": 51, "29028d": 51, "30525d": 51, "00944d": 51, "15516d": 51, "03807d": 51, "04783d": 51, "62300d": 51, "97566d": 51, "23925d": 51, "89135d": 51, "19500d": 51, "82752d": 51, "02205d": 51, "79721d": 51, "18852d": 51, "77513d": 51, "32701d": 51, "75961d": 51, "92977d": 51, "74777d": 51, "63936d": 51, "73929d": 51, "87805d": 51, "73332d": 51, "00035d": 51, "72974d": 51, "60231d": 51, "72751d": 51, "69327d": 51, "72575d": 51, "20291d": 51, "72450d": 51, "99396d": 51, "72328d": 51, "45785d": 51, "72250d": 51, "66249d": 51, "72197d": 51, "88656d": 51, "72131d": 51, "59536d": 51, "72047d": 51, "53286d": 51, "71976d": 51, "43617d": 51, "71928d": 51, "20744d": 51, "71874d": 51, "19581d": 51, "57358d": 51, "71815d": 51, "80283d": 51, "71800d": 51, "86547d": 51, "71792d": 51, "92775d": 51, "1750": 51, "71787d": 51, "79399d": 51, "1800": [51, 62], "71785d": 51, "37693d": 51, "1850": 51, "71783d": 51, "12377d": 51, "1900": [51, 62], "71782d": 51, "58807d": 51, "1950": [51, 62], "71781d": 51, "27521d": 51, "71780d": 51, "01838d": 51, "2140": [51, 52], "018d": 51, "718d": 51, "178028020708659": 51, "86408": 51, "93467": 51, "86262": 51, "75081": 51, "96981": 51, "53054": 51, "11149": 51, "74912": 51, "21307": 51, "9346736406655387": 51, "9698064672110547": 51, "7491181736855458": 51, "iv_list": 51, "460": 51, "91729d": 51, "27078d": 51, "05481d": 51, "93334d": 51, "20108d": 51, "94272d": 51, "67145d": 51, "18349d": 51, "42325d": 51, "92998d": 51, "28052d": 51, "52055d": 51, "12258d": 51, "51169d": 51, "96203d": 51, "03021d": 51, "86267d": 51, "21595d": 51, "81482d": 51, "72608d": 51, "79072d": 51, "26377d": 51, "77769d": 51, "26844d": 51, "76880d": 51, "81014d": 51, "75912d": 51, "54230d": 51, "74843d": 51, "73878d": 51, "66023d": 51, "80375d": 51, "72000d": 51, "29436d": 51, "71556d": 51, "57365d": 51, "71109d": 51, "92874d": 51, "70677d": 51, "03134d": 51, "70264d": 51, "65964d": 51, "70021d": 51, "94705d": 51, "69893d": 51, "90922d": 51, "69794d": 51, "15579d": 51, "69724d": 51, "61087d": 51, "69680d": 51, "38448d": 51, "69652d": 51, "08162d": 51, "69621d": 51, "89696d": 51, "69592d": 51, "00189d": 51, "69560d": 51, "52089d": 51, "69537d": 51, "50911d": 51, "69521d": 51, "23773d": 51, "69512d": 51, "88230d": 51, "69506d": 51, "76983d": 51, "69502d": 51, "08849d": 51, "69499d": 51, "98787d": 51, "69495d": 51, "53047d": 51, "69491d": 51, "12177d": 51, "69488d": 51, "45673d": 51, "2141": 51, "457d": 51, "695d": 51, "948765982874498": 51, "q_mu_unwhiten": 51, "q_var_unwhiten": 51, "set_xtick": 51, "minor": 51, "set_ytick": 51, "listwrapp": 51, "0x7fcfbdb1ce80": 51, "0x7fcf98618700": 51, "0x7fcf98618520": 51, "rememb": [51, 57, 58, 62, 67, 69], "leq": 51, "With": [51, 52, 59, 62, 63, 69], "setup": [51, 67], "mu_f": 51, "mu_g": 51, "sigma_f": 51, "sigma_g": 51, "uf": [51, 54, 65, 69], "initialis": [51, 57, 58, 62], "mxl": 51, "lxmxm": 51, "298": 51, "44521d": 51, "62929d": 51, "17536d": 51, "85678d": 51, "84264d": 51, "74463d": 51, "18739d": 51, "20540d": 51, "03397d": 51, "37977d": 51, "35736d": 51, "19784d": 51, "85507d": 51, "90258d": 51, "38568d": 51, "18620d": 51, "06028d": 51, "83948d": 51, "44384d": 51, "64975d": 51, "90463d": 51, "77259d": 51, "55241d": 51, "50941d": 51, "41403d": 51, "54117d": 51, "67700d": 51, "88611d": 51, "19464d": 51, "68109d": 51, "86225d": 51, "10662d": 51, "55773d": 51, "86343d": 51, "02080d": 51, "48201d": 51, "64970d": 51, "93980d": 51, "47558d": 51, "81754d": 51, "34171d": 51, "41515d": 51, "26776d": 51, "10931d": 51, "21259d": 51, "60048d": 51, "13337d": 51, "38712d": 51, "02389d": 51, "74448d": 51, "45899d": 51, "74669d": 51, "89688d": 51, "71870d": 51, "30694d": 51, "65540d": 51, "87407d": 51, "00173d": 51, "49752d": 51, "18554d": 51, "27385d": 51, "23276d": 51, "09314d": 51, "69974d": 51, "97240d": 51, "40155d": 51, "87100d": 51, "30062d": 51, "77038d": 51, "07311d": 51, "67227d": 51, "13528d": 51, "59190d": 51, "66881d": 51, "50920d": 51, "86379d": 51, "43698d": 51, "26855d": 51, "37257d": 51, "48417d": 51, "32587d": 51, "10780d": 51, "2193": 51, "108d": 51, "326d": 51, "63258728580373713": 51, "noteworthi": 51, "indepedentlat": 51, "bf": 51, "parent": 51, "decid": 51, "complex": [51, 64, 67, 74], "did": [51, 55, 56, 58, 65], "child": 51, "forc": [51, 54, 62], "goal": 51, "exploit": 51, "saw": 51, "slower": [51, 72], "tailor": [51, 58, 67], "thank": 51, "outsid": [51, 52, 54, 55, 68], "amount": [51, 56], "fully_correlated_condit": 51, "ineffici": 51, "mp": 51, "sens": [51, 57, 73], "redund": 51, "behavior": [51, 58], "independent_interdomain_condit": 51, "proactiv": 51, "inspect_condit": 51, "inducing_variable_typ": 51, "kernel_typ": 51, "string": 51, "linenumb": 51, "info": [51, 65], "getmemb": 51, "__code__": 51, "wrapped_funct": 51, "0x7fcfc0343730": 51, "check_shap": [51, 54, 55, 60, 62], "118": 51, "xisqrtmeanvar": 52, "adam_learning_r": 52, "autotun": [52, 65], "501406": 52, "662613": 52, "662647": 52, "697183": 52, "403137": 52, "403204": 52, "403212": 52, "040037": 52, "040073": 52, "040092": 52, "040361": 52, "139": 52, "5640": 52, "unit": [52, 62, 67], "426": 52, "9017": 52, "guess": 52, "fact": [52, 57], "variational_param": 52, "5641": 52, "trick": 52, "forbid": 52, "adam_opt_for_vgp": 52, "adam_opt_for_gpr": 52, "04f": 52, "2548": 52, "9456": 52, "6363": 52, "3270": 52, "0177": 52, "2581": 52, "9489": 52, "6397": 52, "3305": 52, "0213": 52, "9687": 52, "227": 52, "9840": 52, "3326": 52, "8429": 52, "data_minibatch": 52, "prefetch": [52, 65], "data_minibatch_it": 52, "svgp_object": 52, "averag": [52, 62, 65], "136": 52, "home": [52, 65, 72], "compromis": 52, "svgp_ordinari": 52, "svgp_natgrad": 52, "ordinary_adam_opt": 52, "optimize_tensor": 52, "natgrad_adam_opt": 52, "svgp_ordinary_loss": 52, "svgp_natgrad_loss": 52, "7712": 52, "0862": 52, "guarante": 52, "situat": 52, "y_binari": 52, "vgp_data": 52, "vgp_bernoulli": 52, "vgp_bernoulli_natgrad": 52, "142": 52, "8380": 52, "vgp_bernoulli_natgrads_xi": 52, "persist": 52, "tape": [52, 64], "record": 52, "memori": [52, 63, 66], "143": 52, "0989": 52, "shouldn": 52, "vpg": 53, "087486": 53, "214809": 53, "214835": 53, "243745": 53, "894435": 53, "894501": 53, "894509": 53, "quantit": 53, "round": 53, "asarrai": 53, "twinx": 53, "09": [53, 59, 66], "530021": 53, "530047": 53, "530065": 53, "530303": 53, "487473214735196": 53, "000e": [53, 54], "362e": 53, "467e": 53, "450e": 53, "701e": 53, "637e": 53, "499e": 53, "853e": 53, "116": [53, 54], "233x233": 53, "y_data": 53, "line2d": 53, "0x7fe7705640d0": 53, "pred_log_dens": 53, "ytest": [53, 68], "full_lik": 53, "interpol": 53, "nearest": 53, "extent": 53, "aspect": 53, "auto": 53, "cmap": [53, 58, 67], "cm": [53, 58], "viridi": 53, "colorbar": 53, "scalex": 53, "scalei": 53, "0x7fe780716fe0": 53, "x_new": 53, "y_new": 53, "dens_new": 53, "barcontain": 53, "artist": 53, "incorpor": [54, 74], "durrand": 54, "solin": 54, "meant": [54, 59], "complet": [54, 62, 67, 74], "vff": 54, "lose": 54, "noth": 54, "dedic": 54, "commun": 54, "tensorlik": 54, "227375": 54, "384892": 54, "384922": 54, "416424": 54, "041252": 54, "041318": 54, "041326": 54, "linearoper": 54, "blockdiag": 54, "linalg": [54, 64], "linearoperatorblockdiag": 54, "linearoperatordiag": 54, "lowrank": 54, "linearoperatorlowrankupd": 54, "u_m": 54, "phi_m": 54, "eq": 54, "onto": 54, "truncat": [54, 65], "basi": [54, 58], "omega_1": 54, "omega_m": 54, "fourierfeatures1d": 54, "\u03c9_m": 54, "2\u03c0": 54, "cosin": 54, "sine": [54, 60], "mathrm": 54, "operatornam": 54, "u_": 54, "matern12": [54, 58, 60], "kuu_matern12_fourierfeatures1d": 54, "omega": 54, "lamb": 54, "two_or_four": 54, "d_co": 54, "v_co": 54, "110": 54, "cosine_block": 54, "is_positive_definit": 54, "not_equ": 54, "d_sin": 54, "113": 54, "sine_block": 54, "kuf_matern12_fourierfeatures1d": 54, "kuf_co": 54, "omegas_sin": 54, "kuf_sin": 54, "left_tail": 54, "right_tail": 54, "replac": [54, 59, 62, 71], "concat": 54, "kuu_matern32_fourierfeatures1d": 54, "four_or_eight": 54, "pow": 54, "115": 54, "v_sin": 54, "kuf_matern32_fourierfeatures1d": 54, "freq": 54, "tail_co": 54, "delta_x": 54, "tail_sin": 54, "principl": [54, 58, 62], "prior_kl": 54, "prior_kl_vff": 54, "gauss_kl_vff": 54, "methjod": 54, "solv": [54, 59, 62], "log_abs_determin": 54, "n\u2080": 54, "n\u2081": 54, "\u00bd": 54, "\u03c3\u2081": 54, "\u03c3\u2080": 54, "\u03bc\u2081": 54, "\u03bc\u2080": 54, "\u1d40": 54, "ln": 54, "det": 54, "q_sqrt\u1d40a": 54, "q_mu\u1d40": 54, "logdet": 54, "m\u00b2": 54, "kinv_q_mu": 54, "mahalanobis_term": 54, "transpose_a": 54, "logdet_prior": 54, "product_of_dimensions__int": 54, "reduce_prod": [54, 65], "constant_term": 54, "lq": 54, "band_part": 54, "triangl": [54, 59], "logdet_q": 54, "reduce_sum": [54, 67], "diag_part": 54, "transpose_b": 54, "trace_term": 54, "n\u00b2": 54, "n\u00b3": 54, "twokl": 54, "vffposterior": 54, "_conditional_fus": 54, "minibatch": 54, "_q_dist": 54, "num_func": 54, "kuuinv_kuf": 54, "kuft_kuuinv_kuf_diag": 54, "expand_dim": 54, "get_shap": 54, "lta": 54, "won": [54, 55], "elif": 54, "matrix_band_part": 54, "a_til": 54, "float_typ": 54, "todo": 54, "densematrix": 54, "atl": 54, "bad": [54, 60], "kuuinv_qsqrt": 54, "kuuinv_covu_kuuinv": 54, "to_dens": 54, "precomputedvalu": 54, "_conditional_with_precomput": 54, "qinv_kuf": 54, "kuft_qinv_kuf_diag": 54, "get_posterior_class": 54, "_get_posterior_vff": 54, "short": 54, "hand": [54, 62], "mf": 54, "tril": 54, "conditional_f_mean": 54, "conditional_f_var": 54, "posterior_f_mean": 54, "posterior_f_var": 54, "assert_array_equ": 54, "461594": 54, "461619": 54, "461638": 54, "461897": 54, "precomputed_posterior_f_mean": 54, "precomputed_posterior_f_var": 54, "assert_allclos": 54, "510": 54, "501": 54, "fnew": 54, "noise_scal": [54, 55], "mfreq": 54, "5000": 54, "aparameterident": 54, "18351": 54, "bparameterident": 54, "float644": [54, 57], "18402": 54, "89075": 54, "35057e": 54, "00000e": 54, "m_ip": 54, "93002": 54, "96123": 54, "165e": 54, "m_ref": 54, "anyth": [54, 56, 62, 63], "exact_gpr_lml": 54, "ip_svgp_elbo": 54, "vff_svgp_elbo": 54, "402": 54, "2158074486284": 54, "365": 54, "31215466596103": 54, "171": [54, 56, 59, 61, 63], "03923686986113": 54, "plot_data": 54, "2_i": 55, "come": [55, 61, 62, 63], "third": 55, "simplefilt": 55, "tf_cpp_min_log_level": 55, "inherit_check_shap": [55, 60], "gf": 55, "optimizer_config": 55, "x_plot": 55, "101": 55, "anyndarrai": 55, "mean_plot": 55, "var_plot": 55, "x_err": 55, "mean_err": 55, "var_err": 55, "get_confidence_bound": 55, "lower_plot": 55, "upper_plot": 55, "lower_err": 55, "upper_err": 55, "vline": 55, "synthet": 55, "amongst": 55, "default_rng": [55, 59], "standard_norm": 55, "alon": [55, 58], "look": [55, 58, 59, 60, 61, 62, 64, 66, 74], "12365": 55, "61646": 55, "0057": 55, "underestim": 55, "overestim": [55, 57], "24138": 55, "77092": 55, "14643": 55, "47433": 55, "47147": 55, "fidel": 55, "Of": [55, 63], "cours": [55, 63], "stick": 55, "simplic": [55, 64, 66], "get_group": 55, "generate_grouped_data": 55, "raw": [55, 62, 63], "66418": 55, "2537": 55, "18977": 55, "x_and_group": 55, "x_plot_and_group": 55, "wouldn": 55, "strictli": 55, "switchedfunct": 55, "81565": 55, "30409": 55, "cparameterident": 55, "01012": 55, "25862": 55, "measur": [55, 62], "n_repeat": 55, "generate_empiricial_noise_data": 55, "y_mean": [55, 56, 57, 59, 62, 63], "keepdim": 55, "y_var": [55, 56, 57, 59, 62, 63], "sake": 55, "x_flat": 55, "broadcast_to": 55, "y_flat": 55, "occupi": 55, "inject": [55, 62], "somewhat": 55, "develop": [55, 58, 62], "confid": [55, 56], "vertic": 55, "5174": 55, "24234": 55, "02477": 55, "y_mean_mean": 55, "y_mean_var": 55, "enough": [55, 59, 60, 62, 65, 72], "fixedvarianceofmean": 55, "var_mean": 55, "tensortyp": [55, 60], "plug": [55, 62], "60614": 55, "26903": 55, "themselv": [55, 62], "chapter": [56, 57, 58, 59, 60, 61, 62, 63], "concept": [56, 58], "perfectli": [56, 62, 72], "epistem": 56, "matter": 56, "never": 56, "aleator": 56, "865": [56, 59, 61, 63], "666": [56, 59, 61, 63], "804": [56, 59, 61, 63], "771": [56, 59, 61, 63], "147": [56, 59, 61, 63], "866": [56, 59, 61, 63], "007": [56, 59, 61, 63], "026": [56, 59, 61, 63], "889": [56, 59, 61, 63], "028": [56, 59, 61, 63], "plu": 56, "think": 56, "28009566": 56, "30584767": 56, "54585965": 56, "xplot": [56, 57, 58, 59, 60, 62, 63], "f_lower": [56, 58, 60], "f_upper": [56, 58, 60], "y_lower": [56, 57, 59, 62, 63], "y_upper": [56, 57, 59, 62, 63], "awai": [56, 60], "certain": 56, "li": 56, "smooth": [56, 58], "x_2": 56, "nearbi": 56, "75907766": 56, "71506022": 56, "17286964": 56, "11372553": 56, "relationship": 56, "18033224": 56, "04013752": 56, "12780391": 56, "former": 56, "prefer": [56, 68], "gave": 56, "quick": [56, 73], "talk": [57, 60, 62, 63], "seen": [57, 72, 74], "far": [57, 58, 62], "nrow": [57, 58, 59, 60, 62, 63], "ncol": [57, 58, 59, 60, 62, 63], "mean_lin": [57, 58, 59, 60, 62, 63], "outlier": [57, 67], "light": 57, "struggl": [57, 59, 67], "177": 57, "183": [57, 67], "428": 57, "838": 57, "827": 57, "293": 57, "270": 57, "031": 57, "39101": 57, "60446": 57, "02437": 57, "middl": [57, 62], "student": 57, "heavier": 57, "affect": [57, 58, 62], "studentt": 57, "float645": 57, "04051": 57, "2941": 57, "05426": 57, "16600e": 57, "3120e": 57, "beween": 57, "squish": 57, "trial": 57, "encapsul": 57, "218": 57, "453": 57, "638": 57, "523": 57, "541": 57, "455": 57, "632": 57, "309": 57, "330": [57, 63], "868": 57, "706": 57, "672": 57, "742": 57, "813": 57, "617": 57, "456": 57, "730": 57, "841": 57, "massag": 57, "concaten": 57, "18082": 57, "34063": 57, "2730e": 57, "5364e": 57, "bewar": [57, 58], "symmetr": 57, "harder": [57, 67], "fsampl": 57, "psampl": 57, "c1": [57, 70], "03717187": 57, "sim3": 57, "chanc": 57, "multiclass": [57, 65, 74], "sparsiti": 57, "studi": [57, 58, 70], "17754": 57, "34069": 57, "21133": 57, "9278": 57, "4616": 57, "truli": 57, "huge": 57, "frustrat": 57, "train_generic_model": 57, "regressiondata": 57, "deepcopi": 58, "coolwarm": 58, "primari": [58, 60, 61, 69], "coordin": 58, "intuit": 58, "behav": [58, 66], "vist": 58, "investig": [58, 72], "plot_kernel_sampl": 58, "20220903": 58, "n_sampl": [58, 67], "__class__": [58, 66, 70], "__name__": [58, 66, 70], "set_ylim": [58, 67, 71], "bottom": 58, "plot_kernel_predict": 58, "plot_kernel": 58, "samples_ax": 58, "prediction_ax": 58, "cover": [58, 73], "popular": 58, "smoother": 58, "toward": [58, 60], "infti": 58, "smoothn": 58, "infinit": 58, "radial": 58, "ideal": [58, 73], "worri": 58, "impact": [58, 59, 61, 67], "rst": 58, "__": [58, 72], "region": 58, "rapid": 58, "transit": 58, "coupl": [58, 62, 67], "rare": 58, "stright": 58, "necessarli": 58, "straight": 58, "Or": [58, 60, 62], "pattern": [58, 67], "trend": [58, 62, 64], "polynomi": [58, 60], "great": [58, 62], "complic": [58, 62], "topic": [58, 64, 74], "plot_2d_kernel_sampl": 58, "n_grid": [58, 59], "xplot1": [58, 59], "xplot2": [58, 59], "meshgrid": [58, 59], "plot_surfac": 58, "plot_2d_kernel_predict": 58, "hide": 58, "plot_2d_kernel": 58, "subplot_kw": 58, "customis": 58, "prohibit": 59, "predicit": 59, "getattr": 59, "marker": 59, "float6411": 59, "6466": 59, "37333": 59, "24001": 59, "gain": 59, "ish": 59, "put": [59, 65], "four": 59, "evenli": 59, "125": 59, "375": 59, "625": 59, "875": [59, 62], "79179": 59, "38665": 59, "24753": 59, "21006": 59, "excel": [59, 67], "irregularli": 59, "float646": 59, "99571": 59, "09965": 59, "57999": 59, "12846": 59, "82829": 59, "overli": [59, 67], "simplist": 59, "compens": [59, 64], "plot_2d_model": 59, "ax_mean": 59, "ax_std": 59, "y_std": 59, "pcolor": 59, "red": [59, 69], "1234": 59, "n_induc": 59, "algoritm": [59, 62], "cluster": [59, 65], "vq": [59, 65], "kmean": 59, "corner": 59, "yet": 59, "access": [59, 62, 63], "circumst": 59, "n_dim": 59, "sample_halton_sequ": 59, "robustgp": 59, "repositori": [59, 72], "didn": 60, "min_x": 60, "max_x": 60, "hline": 60, "linestyl": 60, "revert": 60, "plenti": 60, "happili": 60, "extrapol": 60, "extern": 60, "speak": 60, "mislead": 60, "sinemeanfunct": 60, "wave": 60, "dive": 61, "get_model": 61, "monitortask": 61, "monitortaskgroup": [61, 63], "monitoringtask": 61, "my_callback": 61, "hello": 61, "execute_task": 61, "export": 61, "progress": 61, "modeltotensorboard": 61, "entir": [61, 62, 63], "logdir": 61, "reload_multifil": 61, "scalartotensorboard": 61, "my_scalar": 61, "5778089200757": 61, "scalar_task": 61, "my_scalar_nam": 61, "imagetotensorboard": 61, "my_imag": 61, "ypred": 61, "isol": 61, "my_image_nam": 61, "my_scalar_2": 61, "my_image_2": 61, "fast_task_group": 61, "slow_task_group": 61, "redefin": 61, "had": 61, "hardcod": 61, "panda": 62, "pd": 62, "fundament": 62, "leaf": 62, "node": 62, "tune": [62, 71], "linearmodel": 62, "slope": 62, "n_input": 62, "n_output": 62, "tensordata": 62, "super": [62, 65, 66, 67], "n_row": 62, "Being": 62, "obviou": 62, "comfort": 62, "trane": 62, "saniti": [62, 74], "slopeparameterident": 62, "__main__": 62, "0x7f849138d900": 62, "programmat": 62, "2x_": 62, "i0": 62, "3x_": 62, "i1": 62, "x_train": 62, "y_train": 62, "y_predict": 62, "squared_error": 62, "reduce_mean": 62, "Be": 62, "rule": 62, "fine": 62, "thousand": [62, 74], "atmospher": 62, "mauna": 62, "loa": 62, "observatori": 62, "hawaii": 62, "co2_data": 62, "read_csv": 62, "gml": 62, "noaa": 62, "gov": 62, "webdata": 62, "ccgg": 62, "co2": 62, "co2_mm_mlo": 62, "csv": 62, "comment": 62, "xco2": 62, "decim": 62, "date": 62, "yco2": 62, "plot_co2_model_predict": 62, "idx_plot": 62, "opt_opt": 62, "plot_co2_kernel": 62, "2050": 62, "2030": 62, "favourit": 62, "float6492563": 62, "0481": 62, "72403": 62, "zoom": 62, "yearli": 62, "cycl": [62, 64], "float64267": 62, "609": 62, "9668": 62, "float64394": 62, "695": 62, "1521": 62, "0113": 62, "1637": 62, "huh": 62, "simplest": 62, "init": 62, "got": 62, "280_000": 62, "140": 62, "float64280000": 62, "1307": 62, "0345": 62, "99962": 62, "35551": 62, "whatsev": 62, "possibli": 62, "belief": 62, "long_term_kernel": 62, "lognorm": 62, "periodic_kernel": 62, "lognormaltru": 62, "float641448": 62, "107": 62, "319": 62, "float641235": 62, "8967": 62, "99951": 62, "96115": 62, "chose": [62, 72], "enforc": 62, "sent": 62, "untransform": 62, "unconstrained_vari": 62, "049787068367863944": 62, "softclip": 62, "200_000": 62, "400_000": 62, "parametersoftclip": 62, "002": 62, "046": 62, "4394": 62, "3743": 62, "3989": 62, "32223": 62, "46551": 62, "untrain": 62, "tool": [62, 64], "softer": 62, "subsect": 62, "past": 62, "simpler": 62, "0433": 62, "2_000": 62, "991": 62, "6642977575946": 62, "971": 62, "9966050581327": 62, "955": 62, "9235899627175": 62, "941": 62, "8264800582791": 62, "929": 62, "5120554572727": 62, "918": 62, "8361514846966": 62, "909": 62, "6866938618355": 62, "901": 62, "964521983764": 62, "895": 62, "5713043390281": 62, "890": 62, "3847292264635": 62, "886": 62, "2777099025883": 62, "883": 62, "1066825361156": 62, "880": 62, "6997907009928": 62, "878": 62, "9078598316937": 62, "877": 62, "5806437314469": 62, "876": 62, "5821507939008": 62, "8113091192704": 62, "1906208195325": 62, "874": 62, "6589537407192": 62, "1856815351891": 62, "float64280002": 62, "137": 62, "551": 62, "80473": 62, "55247": 62, "restor": 63, "techniqu": 63, "infrastructur": 63, "savedmodel": 63, "mechan": 63, "box": 63, "checkpointmanag": 63, "initial_valu": 63, "checkpoints_0": 63, "ckpt": 63, "max_to_keep": 63, "old": 63, "latest_checkpoint": 63, "checkpoints_1": 63, "checkpoints_2": 63, "checkpoint_task": 63, "executecallback": 63, "verifi": 63, "remeb": 63, "hasattr": 63, "compiled_predict_f": 63, "input_signatur": 63, "tensorspec": 63, "compiled_predict_i": 63, "save_dir": 63, "saved_model_0": 63, "loaded_model": 63, "multiple_assign": [63, 72], "model_0": 63, "646614675731874": 63, "3733319087937649": 63, "chain_of_shift_of_softplu": 63, "24001197623266737": 63, "model_1": 63, "params_0": 63, "present": [63, 67], "resum": 63, "disk": 63, "disadvantag": 63, "lot": 63, "lost": 63, "instanti": 63, "metatask": 64, "fortuin": 64, "r\u00e4tsch": 64, "705976": 64, "851529": 64, "851556": 64, "882042": 64, "614879": 64, "614955": 64, "614967": 64, "meta": 64, "realiz": 64, "num_funct": 64, "609329": 64, "609360": 64, "609382": 64, "609666": 64, "generate_meta_and_test_task": 64, "num_datapoint": 64, "num_meta": 64, "num_test": 64, "d_i": 64, "tild": 64, "sd": 64, "n_i": 64, "rand_indic": 64, "train_i": 64, "sort": 64, "test_i": 64, "train_x": 64, "traininig": 64, "test_x": 64, "num_meta_task": 64, "num_test_task": 64, "num_data_per_task": 64, "num_it": 64, "build_mean_funct": 64, "backend": 64, "set_floatx": 64, "relu": [64, 65, 67], "boil": 64, "down": 64, "preval": 64, "across": [64, 74], "build_model": 64, "create_optimization_step": 64, "watch_accessed_vari": 64, "watch": 64, "grad": 64, "apply_gradi": 64, "train_loop": 64, "meta_task": 64, "took": 64, "2f": 64, "mean_function_optim": 64, "test_model": 64, "metric": 64, "mean_squared_error": 64, "y_pred": 64, "test_task": 64, "pred_mean": 64, "pred_var": 64, "linewidth": 64, "facecolor": 64, "ko": 64, "markers": 64, "mse": 64, "mean_ms": 64, "std_mse": 64, "gunnar": 64, "1901": 64, "08098": 64, "tensorflow_dataset": 65, "kmeans2": 65, "198786": 65, "344719": 65, "344749": 65, "376775": 65, "053068": 65, "053133": 65, "053141": 65, "original_dataset": 65, "mnist": 65, "split": [65, 67, 73], "with_info": 65, "total_num_data": 65, "num_exampl": 65, "image_s": 65, "input_slic": 65, "255": 65, "1024": 65, "drop_remaind": 65, "num_parallel_cal": 65, "418022": 65, "cloud": 65, "google_auth_provid": 65, "184": 65, "googl": 65, "authent": 65, "bearer": 65, "token": 65, "empti": 65, "not_found": 65, "credenti": 65, "gce": 65, "failed_precondit": 65, "request": 65, "libcurl": 65, "couldn": 65, "resolv": 65, "metadata": 65, "download": 65, "prepar": 65, "mib": 65, "circleci": [65, 72], "128632": 65, "128668": 65, "128692": 65, "128989": 65, "convnet": 65, "20k": 65, "kernelwithconvnn": 65, "name_scop": 65, "input_s": 65, "input_shap": 65, "cnn": 65, "sequenti": 65, "inputlay": 65, "conv2d": 65, "filter": 65, "pad": 65, "maxpool2d": 65, "pool_siz": 65, "stride": 65, "a_input": 65, "b_input": 65, "transformed_a": 65, "transformed_b": 65, "convnn": 65, "multidispatch": 65, "kernelspaceinducingpoint": 65, "readi": [65, 69], "num_mnist_class": 65, "num_inducing_point": 65, "images_subset": 65, "labels_subset": 65, "inducing_variable_kmean": 65, "minit": 65, "inducing_variable_cnn": 65, "058536": 65, "cache_dataset_op": 65, "856": 65, "unexpect": 65, "partial": 65, "content": 65, "discard": 65, "pipelin": 65, "data_iter": 65, "haven": 65, "pred": 65, "8320": 65, "brownian": [66, 74], "motion": [66, 74], "863178": 66, "040613": 66, "040651": 66, "075593": 66, "998472": 66, "998572": 66, "998583": 66, "adequ": 66, "stationari": 66, "isotropicstationari": 66, "docstr": 66, "anisotropicstationari": 66, "superclass": 66, "convent": 66, "command": 66, "k_brownian": 66, "675053": 66, "675104": 66, "675130": 66, "675463": 66, "plotkernelfunct": 66, "1f": 66, "littl": [66, 73], "33113": 66, "28387": 66, "blog": 67, "post": 67, "prototyp": 67, "varieti": 67, "ml": 67, "examin": [67, 68], "imagin": 67, "get_cmap": 67, "noise_std": 67, "0e": 67, "sinusoidal_data": 67, "ro": [67, 68], "sight": 67, "seem": 67, "multilay": 67, "cde": 67, "reveal": 67, "world": 67, "taxi": 67, "drop": 67, "passeng": 67, "destin": 67, "airport": 67, "citi": 67, "suburb": 67, "net": 67, "mog": 67, "characterist": 67, "mu_m": 67, "sigma_m": 67, "pi_m": 67, "pi_": 67, "mu_": 67, "sigma_": 67, "triangleq": [67, 69], "prod_": 67, "y_n": [67, 73], "bias": 67, "reinvent": 67, "wheel": 67, "interact": 67, "977763": 67, "107737": 67, "107763": 67, "136949": 67, "806458": 67, "806521": 67, "806529": 67, "datahold": 67, "paramlist": 67, "_build_likelihood": 67, "num_mixtur": 67, "inner_dim": 67, "hidden": 67, "_mixtur": 67, "_create_network": 67, "dim_in": 67, "dim_out": 67, "init_xavier_std": 67, "eval_network": 67, "log_probs_mog": 67, "reduce_logsumexp": 67, "compli": 67, "restrict": 67, "ge": 67, "foral": 67, "xavier": 67, "glorot": 67, "bengio": 67, "earlier": 67, "18385": 67, "01075": 67, "05168": 67, "17194": 67, "00571": 67, "07995": 67, "08247": 67, "37778": 67, "09596": 67, "551607": 67, "551634": 67, "551672": 67, "551937": 67, "adagrad": 67, "adadelta": 67, "131": 67, "58194782932202": 67, "ensembl": 67, "mdn_plot": 67, "sphinx": 67, "set_xlim": [67, 70, 71], "scikit": 67, "sklearn": 67, "make_moon": 67, "moon_data": 67, "10e3": 67, "9142768444019": 67, "ncrg": 67, "4288": 67, "aston": 67, "birmingham": 67, "uk": 67, "1994": 67, "fitcvsvf": [68, 72], "gettrainingtestdata": [68, 72], "plotcomparisonfigur": 68, "plotpredict": 68, "printmodelparamet": 68, "repeatminim": 68, "stretch": 68, "clutter": 68, "902445": 68, "038364": 68, "038390": 68, "068208": 68, "755434": 68, "755501": 68, "755509": 68, "xtrain": 68, "ytrain": 68, "getkernel": 68, "exact_model": 68, "tol": [68, 71], "figa": 68, "443559": 68, "443584": 68, "443604": 68, "443842": 68, "074285": 68, "90049": 68, "5825": 68, "initializehyperparametersfromexactsolut": 68, "sparse_model": 68, "perfect": 68, "vfemodel": 68, "vfecb": 68, "eval_func": 68, "_tf_eval": 68, "0x7f530847c4c0": 68, "trigger": 68, "retrac": 68, "expens": [68, 74], "excess": 68, "repeatedli": 68, "reduce_retrac": 68, "unnecessari": 68, "www": 68, "controlling_retrac": 68, "api_doc": 68, "0x7f53085bd870": 68, "074286": 68, "fitcmodel": 68, "fitccb": 68, "018996": 68, "3297": 68, "61727": 68, "stai": 68, "eventu": 68, "wors": 68, "figb": 68, "finish": 68, "vfeiter": 68, "n_iter": 68, "vfelog_likelihood": 68, "vfehold_out_likelihood": 68, "hold_out_likelihood": 68, "fontdict": 68, "fontsiz": 68, "probabilist": [68, 74], "bauer": 68, "march": 69, "alex": 69, "decemb": 69, "clarifi": 69, "geq": 69, "q_": 69, "tfrac": 69, "fu": 69, "remaind": 69, "star": [69, 73], "woodburi": 69, "eigenvalu": [69, 73], "phantom": 69, "lemma": [69, 73], "aa": 69, "l_": 69, "l_bl_b": 69, "concurr": 69, "uai": 69, "bay": 70, "collaps": [70, 72], "810470": 70, "950775": 70, "950798": 70, "980326": 70, "790493": 70, "790565": 70, "790574": 70, "m1": 70, "m2": 70, "m3": 70, "m4": 70, "m5": 70, "m6": 70, "918619": 70, "918646": 70, "918665": 70, "918905": 70, "loss_closur": 70, "everyth": 70, "plan": 70, "sharei": 70, "c2": 70, "c3": 70, "c4": 70, "c5": 70, "5g": 70, "0774": 70, "82561": 70, "16002": 70, "0773": 70, "82546": 70, "82549": 70, "16003": 70, "83436136005674": 70, "834361541124224": 70, "834400091469195": 70, "83439998906201": 70, "834354780715604": 70, "cglb": 71, "load_snelson_data": 71, "090192": 71, "223327": 71, "223347": 71, "252175": 71, "943897": 71, "943967": 71, "943976": 71, "snelson1d": 71, "empir": 71, "landscap": 71, "iv_indic": 71, "loss_with_changed_paramet": 71, "losses_fn": 71, "gpr_obj": 71, "sgpr_obj": 71, "cglb_obj": 71, "842553": 71, "842580": 71, "842599": 71, "842851": 71, "involv": 71, "threshold": 71, "5\u03f5": 71, "confirm": 71, "closer": 71, "wich": 71, "pred_no_tol": 71, "pred_tol": 71, "subplots_adjust": 71, "hspace": 71, "mu_no_tol": 71, "std_no_tol": 71, "tab": 71, "mu_tol": 71, "std_tol": 71, "green": 71, "comprehens": 72, "938923": 72, "063767": 72, "063789": 72, "092735": 72, "730650": 72, "730752": 72, "730760": 72, "isinst": 72, "two_sigma": 72, "full_lml": 72, "328146": 72, "328173": 72, "328193": 72, "328448": 72, "test_n": 72, "vfe_lml": 72, "vupper_lml": 72, "vfe_hyp": 72, "vfe": [72, 74], "optimizewarn": 72, "axhlin": 72, "monoton": 72, "looser": 72, "fm": 72, "fvfe_lml": 72, "fvupper_lml": 72, "init_param": 72, "mismatch": 72, "del": 72, "omit": 72, "pictur": 72, "increasingli": 72, "single_inducing_point": 72, "1260": 72, "487142": 72, "481937": 72, "realli": 72, "rest": [72, 73], "48714176147101": 72, "10776": 72, "float6479859": 72, "76897": 72, "68234": 72, "326": 72, "21603": 72, "diagnos": 72, "lack": 72, "serv": 73, "conclus": 73, "insight": 73, "hat": 73, "advic": 73, "reparameter": 73, "sum_n": 73, "f_n": 73, "trivial": 73, "question": 73, "benefit": 73, "reorganis": 73, "recal": 73, "shorthand": 73, "diagram": 74, "underpin": 74, "codebas": 74, "metalearn": 74, "mixtur": 74, "handli": 74, "gplvm": 74, "fourier": 74}, "objects": {"": [[10, 0, 0, "-", "gpflow"]], "gpflow": [[10, 1, 1, "", "Module"], [10, 1, 1, "", "Parameter"], [0, 0, 0, "-", "base"], [1, 0, 0, "-", "conditionals"], [3, 0, 0, "-", "config"], [4, 0, 0, "-", "covariances"], [10, 4, 1, "", "default_float"], [10, 4, 1, "", "default_int"], [10, 4, 1, "", "default_jitter"], [5, 0, 0, "-", "expectations"], [7, 0, 0, "-", "experimental"], [9, 0, 0, "-", "functions"], [11, 0, 0, "-", "inducing_variables"], [14, 0, 0, "-", "kernels"], [15, 0, 0, "-", "kullback_leiblers"], [16, 0, 0, "-", "likelihoods"], [18, 0, 0, "-", "logdensities"], [21, 0, 0, "-", "models"], [26, 0, 0, "-", "monitor"], [27, 0, 0, "-", "optimizers"], [29, 0, 0, "-", "posteriors"], [30, 0, 0, "-", "probability_distributions"], [32, 0, 0, "-", "quadrature"], [10, 4, 1, "", "set_trainable"], [33, 0, 0, "-", "type_flags"], [34, 0, 0, "-", "utilities"]], "gpflow.Parameter": [[10, 2, 1, "", "assign"], [10, 2, 1, "", "log_prior_density"], [10, 3, 1, "", "trainable"]], "gpflow.base": [[0, 1, 1, "", "PriorOn"]], "gpflow.conditionals": [[1, 4, 1, "", "base_conditional"], [1, 4, 1, "", "uncertain_conditional"], [2, 0, 0, "-", "util"]], "gpflow.conditionals.conditionals": [[1, 4, 1, "", "_dense_conditional"], [1, 4, 1, "", "_sparse_conditional"]], "gpflow.conditionals.multioutput.conditionals": [[1, 4, 1, "", "coregionalization_conditional"], [1, 4, 1, "", "fallback_independent_latent_conditional"], [1, 4, 1, "", "inducing_point_conditional"], [1, 4, 1, "", "separate_independent_conditional"], [1, 4, 1, "", "shared_independent_conditional"]], "gpflow.conditionals.multioutput.sample_conditionals": [[1, 4, 1, "", "_sample_conditional"]], "gpflow.conditionals.sample_conditionals": [[1, 4, 1, "", "_sample_conditional"]], "gpflow.conditionals.util": [[2, 4, 1, "", "base_conditional_with_lm"], [2, 4, 1, "", "expand_independent_outputs"], [2, 4, 1, "", "fully_correlated_conditional"], [2, 4, 1, "", "fully_correlated_conditional_repeat"], [2, 4, 1, "", "independent_interdomain_conditional"], [2, 4, 1, "", "mix_latent_gp"], [2, 4, 1, "", "rollaxis_left"], [2, 4, 1, "", "rollaxis_right"], [2, 4, 1, "", "sample_mvn"], [2, 4, 1, "", "separate_independent_conditional_implementation"]], "gpflow.config": [[3, 1, 1, "", "Config"], [3, 4, 1, "", "as_context"], [3, 4, 1, "", "config"], [3, 4, 1, "", "default_positive_bijector"], [3, 4, 1, "", "default_positive_minimum"], [3, 4, 1, "", "default_summary_fmt"], [3, 4, 1, "", "positive_bijector_type_map"], [3, 4, 1, "", "set_config"], [3, 4, 1, "", "set_default_float"], [3, 4, 1, "", "set_default_int"], [3, 4, 1, "", "set_default_jitter"], [3, 4, 1, "", "set_default_positive_bijector"], [3, 4, 1, "", "set_default_positive_minimum"], [3, 4, 1, "", "set_default_summary_fmt"]], "gpflow.config.Config": [[3, 5, 1, "", "float"], [3, 5, 1, "", "int"], [3, 5, 1, "", "jitter"], [3, 5, 1, "", "positive_bijector"], [3, 5, 1, "", "positive_minimum"], [3, 5, 1, "", "summary_fmt"]], "gpflow.covariances.kufs": [[4, 4, 1, "", "Kuf_conv_patch"], [4, 4, 1, "", "Kuf_kernel_inducingpoints"], [4, 4, 1, "", "Kuf_sqexp_multiscale"]], "gpflow.covariances.kuus": [[4, 4, 1, "", "Kuu_conv_patch"], [4, 4, 1, "", "Kuu_kernel_inducingpoints"], [4, 4, 1, "", "Kuu_sqexp_multiscale"]], "gpflow.covariances.multioutput.kufs": [[4, 4, 1, "", "Kuf_fallback_separate_linear_coregionalization"], [4, 4, 1, "", "Kuf_fallback_shared_linear_coregionalization"], [4, 4, 1, "", "Kuf_generic"], [4, 4, 1, "", "Kuf_separate_linear_coregionalization"], [4, 4, 1, "", "Kuf_separate_separate"], [4, 4, 1, "", "Kuf_separate_shared"], [4, 4, 1, "", "Kuf_shared_linear_coregionalization"], [4, 4, 1, "", "Kuf_shared_separate"], [4, 4, 1, "", "Kuf_shared_shared"]], "gpflow.covariances.multioutput.kuus": [[4, 4, 1, "", "Kuu_fallbace_separate"], [4, 4, 1, "", "Kuu_fallback_separate_shared"], [4, 4, 1, "", "Kuu_fallback_shared"], [4, 4, 1, "", "Kuu_generic"], [4, 4, 1, "", "Kuu_shared_shared"]], "gpflow.expectations": [[5, 4, 1, "", "expectation"], [5, 4, 1, "", "quadrature_expectation"], [6, 0, 0, "-", "quadratures"]], "gpflow.expectations.quadratures": [[6, 4, 1, "", "get_eval_func"]], "gpflow.experimental": [[8, 0, 0, "-", "utils"]], "gpflow.experimental.utils": [[8, 4, 1, "", "experimental"]], "gpflow.functions": [[9, 1, 1, "", "Additive"], [9, 1, 1, "", "Constant"], [9, 1, 1, "", "Function"], [9, 1, 1, "", "Identity"], [9, 1, 1, "", "Linear"], [9, 1, 1, "", "MeanFunction"], [9, 1, 1, "", "Polynomial"], [9, 1, 1, "", "Product"], [9, 1, 1, "", "SwitchedFunction"], [9, 1, 1, "", "SwitchedMeanFunction"], [9, 1, 1, "", "Zero"]], "gpflow.functions.Polynomial": [[9, 2, 1, "", "compute_powers"]], "gpflow.inducing_variables": [[11, 1, 1, "", "FallbackSeparateIndependentInducingVariables"], [11, 1, 1, "", "FallbackSharedIndependentInducingVariables"], [11, 1, 1, "", "InducingPatches"], [11, 1, 1, "", "InducingPoints"], [11, 1, 1, "", "InducingVariables"], [11, 1, 1, "", "MultioutputInducingVariables"], [11, 1, 1, "", "Multiscale"], [11, 1, 1, "", "SeparateIndependentInducingVariables"], [11, 1, 1, "", "SharedIndependentInducingVariables"], [12, 0, 0, "-", "inducing_variables"]], "gpflow.inducing_variables.FallbackSeparateIndependentInducingVariables": [[11, 3, 1, "", "num_inducing"], [11, 3, 1, "", "shape"]], "gpflow.inducing_variables.FallbackSharedIndependentInducingVariables": [[11, 3, 1, "", "num_inducing"], [11, 3, 1, "", "shape"]], "gpflow.inducing_variables.InducingVariables": [[11, 3, 1, "", "num_inducing"], [11, 3, 1, "", "shape"]], "gpflow.inducing_variables.inducing_variables": [[12, 1, 1, "", "InducingPointsBase"]], "gpflow.inducing_variables.inducing_variables.InducingPointsBase": [[12, 3, 1, "", "num_inducing"], [12, 3, 1, "", "shape"]], "gpflow.kernels": [[14, 1, 1, "", "AnisotropicStationary"], [14, 1, 1, "", "ArcCosine"], [14, 5, 1, "", "Bias"], [14, 1, 1, "", "ChangePoints"], [14, 1, 1, "", "Combination"], [14, 1, 1, "", "Convolutional"], [14, 1, 1, "", "Coregion"], [14, 1, 1, "", "Cosine"], [14, 1, 1, "", "Exponential"], [14, 1, 1, "", "IndependentLatent"], [14, 1, 1, "", "IsotropicStationary"], [14, 1, 1, "", "Kernel"], [14, 1, 1, "", "Linear"], [14, 1, 1, "", "LinearCoregionalization"], [14, 1, 1, "", "Matern12"], [14, 1, 1, "", "Matern32"], [14, 1, 1, "", "Matern52"], [14, 1, 1, "", "MultioutputKernel"], [14, 1, 1, "", "Periodic"], [14, 1, 1, "", "Polynomial"], [14, 1, 1, "", "Product"], [14, 5, 1, "", "RBF"], [14, 1, 1, "", "RationalQuadratic"], [14, 1, 1, "", "SeparateIndependent"], [14, 1, 1, "", "SharedIndependent"], [14, 1, 1, "", "Static"], [14, 1, 1, "", "Stationary"], [14, 1, 1, "", "Sum"], [14, 1, 1, "", "White"], [13, 0, 0, "-", "base"]], "gpflow.kernels.AnisotropicStationary": [[14, 2, 1, "", "scaled_difference_matrix"]], "gpflow.kernels.ArcCosine": [[14, 3, 1, "", "ard"]], "gpflow.kernels.Combination": [[14, 3, 1, "", "on_separate_dimensions"]], "gpflow.kernels.Convolutional": [[14, 2, 1, "", "get_patches"]], "gpflow.kernels.IsotropicStationary": [[14, 2, 1, "", "scaled_squared_euclid_dist"]], "gpflow.kernels.Kernel": [[14, 2, 1, "", "on_separate_dims"], [14, 2, 1, "", "slice"], [14, 2, 1, "", "slice_cov"]], "gpflow.kernels.Linear": [[14, 3, 1, "", "ard"]], "gpflow.kernels.LinearCoregionalization": [[14, 2, 1, "", "K"], [14, 2, 1, "", "K_diag"], [14, 3, 1, "", "latent_kernels"], [14, 3, 1, "", "num_latent_gps"]], "gpflow.kernels.MultioutputKernel": [[14, 2, 1, "", "K"], [14, 2, 1, "", "K_diag"], [14, 3, 1, "", "latent_kernels"], [14, 3, 1, "", "num_latent_gps"]], "gpflow.kernels.SeparateIndependent": [[14, 2, 1, "", "K"], [14, 2, 1, "", "K_diag"], [14, 3, 1, "", "latent_kernels"], [14, 3, 1, "", "num_latent_gps"]], "gpflow.kernels.SharedIndependent": [[14, 2, 1, "", "K"], [14, 2, 1, "", "K_diag"], [14, 3, 1, "", "latent_kernels"], [14, 3, 1, "", "num_latent_gps"]], "gpflow.kernels.Stationary": [[14, 3, 1, "", "ard"]], "gpflow.kernels.base": [[13, 1, 1, "", "ReducingCombination"]], "gpflow.kullback_leiblers": [[15, 4, 1, "", "_"], [15, 4, 1, "", "gauss_kl"]], "gpflow.likelihoods": [[16, 1, 1, "", "Bernoulli"], [16, 1, 1, "", "Beta"], [16, 1, 1, "", "Exponential"], [16, 1, 1, "", "Gamma"], [16, 1, 1, "", "Gaussian"], [16, 1, 1, "", "GaussianMC"], [16, 1, 1, "", "HeteroskedasticTFPConditional"], [16, 1, 1, "", "Likelihood"], [16, 1, 1, "", "MonteCarloLikelihood"], [16, 1, 1, "", "MultiClass"], [16, 1, 1, "", "MultiLatentLikelihood"], [16, 1, 1, "", "MultiLatentTFPConditional"], [16, 1, 1, "", "Ordinal"], [16, 1, 1, "", "Poisson"], [16, 1, 1, "", "QuadratureLikelihood"], [16, 1, 1, "", "RobustMax"], [16, 1, 1, "", "ScalarLikelihood"], [16, 1, 1, "", "Softmax"], [16, 1, 1, "", "StudentT"], [16, 1, 1, "", "SwitchedLikelihood"], [17, 0, 0, "-", "utils"]], "gpflow.likelihoods.Likelihood": [[16, 2, 1, "", "conditional_mean"], [16, 2, 1, "", "conditional_variance"], [16, 2, 1, "", "log_prob"], [16, 2, 1, "", "predict_log_density"], [16, 2, 1, "", "predict_mean_and_var"], [16, 2, 1, "", "variational_expectations"]], "gpflow.likelihoods.utils": [[17, 4, 1, "", "inv_probit"]], "gpflow.logdensities": [[18, 4, 1, "", "bernoulli"], [18, 4, 1, "", "beta"], [18, 4, 1, "", "exponential"], [18, 4, 1, "", "gamma"], [18, 4, 1, "", "gaussian"], [18, 4, 1, "", "laplace"], [18, 4, 1, "", "lognormal"], [18, 4, 1, "", "multivariate_normal"], [18, 4, 1, "", "poisson"], [18, 4, 1, "", "student_t"]], "gpflow.models": [[21, 1, 1, "", "BayesianGPLVM"], [21, 1, 1, "", "BayesianModel"], [21, 1, 1, "", "CGLB"], [21, 1, 1, "", "ExternalDataTrainingLossMixin"], [21, 1, 1, "", "GPLVM"], [21, 1, 1, "", "GPMC"], [21, 1, 1, "", "GPModel"], [21, 1, 1, "", "GPR"], [21, 1, 1, "", "GPRFITC"], [21, 1, 1, "", "InternalDataTrainingLossMixin"], [21, 1, 1, "", "SGPMC"], [21, 1, 1, "", "SGPR"], [21, 1, 1, "", "SVGP"], [21, 1, 1, "", "VGP"], [21, 1, 1, "", "VGPOpperArchambeau"], [19, 0, 0, "-", "cglb"], [20, 0, 0, "-", "gpr"], [21, 4, 1, "", "maximum_log_likelihood_objective"], [22, 0, 0, "-", "sgpr"], [23, 0, 0, "-", "svgp"], [21, 4, 1, "", "training_loss"], [21, 4, 1, "", "training_loss_closure"], [24, 0, 0, "-", "util"], [25, 0, 0, "-", "vgp"]], "gpflow.models.BayesianGPLVM": [[21, 2, 1, "", "elbo"], [21, 2, 1, "", "maximum_log_likelihood_objective"], [21, 2, 1, "", "predict_f"], [21, 2, 1, "", "predict_log_density"]], "gpflow.models.BayesianModel": [[21, 2, 1, "", "log_posterior_density"], [21, 2, 1, "", "log_prior_density"], [21, 2, 1, "", "maximum_log_likelihood_objective"]], "gpflow.models.CGLB": [[21, 2, 1, "", "logdet_term"], [21, 2, 1, "", "predict_f"], [21, 2, 1, "", "predict_log_density"], [21, 2, 1, "", "predict_y"], [21, 2, 1, "", "quad_term"]], "gpflow.models.ExternalDataTrainingLossMixin": [[21, 2, 1, "", "training_loss"], [21, 2, 1, "", "training_loss_closure"]], "gpflow.models.GPMC": [[21, 2, 1, "", "log_likelihood"], [21, 2, 1, "", "log_posterior_density"], [21, 2, 1, "", "maximum_log_likelihood_objective"], [21, 2, 1, "", "predict_f"]], "gpflow.models.GPModel": [[21, 2, 1, "", "calc_num_latent_gps"], [21, 2, 1, "", "calc_num_latent_gps_from_data"], [21, 2, 1, "", "predict_f"], [21, 2, 1, "", "predict_f_samples"], [21, 2, 1, "", "predict_log_density"], [21, 2, 1, "", "predict_y"]], "gpflow.models.GPRFITC": [[21, 2, 1, "", "fitc_log_marginal_likelihood"], [21, 2, 1, "", "maximum_log_likelihood_objective"], [21, 2, 1, "", "predict_f"]], "gpflow.models.InternalDataTrainingLossMixin": [[21, 2, 1, "", "training_loss"], [21, 2, 1, "", "training_loss_closure"]], "gpflow.models.SGPMC": [[21, 2, 1, "", "log_likelihood_lower_bound"], [21, 2, 1, "", "log_posterior_density"], [21, 2, 1, "", "maximum_log_likelihood_objective"], [21, 2, 1, "", "predict_f"]], "gpflow.models.VGPOpperArchambeau": [[21, 2, 1, "", "elbo"], [21, 2, 1, "", "maximum_log_likelihood_objective"], [21, 2, 1, "", "predict_f"]], "gpflow.models.cglb": [[19, 1, 1, "", "NystromPreconditioner"], [19, 4, 1, "", "cglb_conjugate_gradient"]], "gpflow.models.gpr": [[20, 1, 1, "", "GPR_deprecated"], [20, 1, 1, "", "GPR_with_posterior"]], "gpflow.models.gpr.GPR_deprecated": [[20, 2, 1, "", "log_marginal_likelihood"], [20, 2, 1, "", "maximum_log_likelihood_objective"], [20, 2, 1, "", "predict_f"]], "gpflow.models.gpr.GPR_with_posterior": [[20, 2, 1, "", "posterior"], [20, 2, 1, "", "predict_f"]], "gpflow.models.sgpr": [[22, 1, 1, "", "SGPRBase_deprecated"], [22, 1, 1, "", "SGPR_deprecated"], [22, 1, 1, "", "SGPR_with_posterior"]], "gpflow.models.sgpr.SGPRBase_deprecated": [[22, 2, 1, "", "upper_bound"]], "gpflow.models.sgpr.SGPR_deprecated": [[22, 1, 1, "", "CommonTensors"], [22, 2, 1, "", "compute_qu"], [22, 2, 1, "", "elbo"], [22, 2, 1, "", "logdet_term"], [22, 2, 1, "", "maximum_log_likelihood_objective"], [22, 2, 1, "", "predict_f"], [22, 2, 1, "", "quad_term"]], "gpflow.models.sgpr.SGPR_deprecated.CommonTensors": [[22, 5, 1, "", "A"], [22, 5, 1, "", "AAT"], [22, 5, 1, "", "B"], [22, 5, 1, "", "L"], [22, 5, 1, "", "LB"], [22, 5, 1, "", "sigma"], [22, 5, 1, "", "sigma_sq"]], "gpflow.models.sgpr.SGPR_with_posterior": [[22, 2, 1, "", "posterior"], [22, 2, 1, "", "predict_f"]], "gpflow.models.svgp": [[23, 1, 1, "", "SVGP_deprecated"], [23, 1, 1, "", "SVGP_with_posterior"]], "gpflow.models.svgp.SVGP_deprecated": [[23, 2, 1, "", "elbo"], [23, 2, 1, "", "maximum_log_likelihood_objective"], [23, 2, 1, "", "predict_f"]], "gpflow.models.svgp.SVGP_with_posterior": [[23, 2, 1, "", "posterior"], [23, 2, 1, "", "predict_f"]], "gpflow.models.util": [[24, 4, 1, "", "data_input_to_tensor"], [24, 4, 1, "", "inducingpoint_wrapper"]], "gpflow.models.vgp": [[25, 1, 1, "", "VGP_deprecated"], [25, 1, 1, "", "VGP_with_posterior"], [25, 4, 1, "", "update_vgp_data"]], "gpflow.models.vgp.VGP_deprecated": [[25, 2, 1, "", "elbo"], [25, 2, 1, "", "maximum_log_likelihood_objective"], [25, 2, 1, "", "predict_f"]], "gpflow.models.vgp.VGP_with_posterior": [[25, 2, 1, "", "posterior"], [25, 2, 1, "", "predict_f"]], "gpflow.monitor": [[26, 1, 1, "", "ExecuteCallback"], [26, 1, 1, "", "ImageToTensorBoard"], [26, 1, 1, "", "ModelToTensorBoard"], [26, 1, 1, "", "Monitor"], [26, 1, 1, "", "MonitorTask"], [26, 1, 1, "", "MonitorTaskGroup"], [26, 1, 1, "", "ScalarToTensorBoard"], [26, 1, 1, "", "ToTensorBoard"]], "gpflow.monitor.ExecuteCallback": [[26, 2, 1, "", "run"]], "gpflow.monitor.ImageToTensorBoard": [[26, 2, 1, "", "run"]], "gpflow.monitor.ModelToTensorBoard": [[26, 2, 1, "", "run"]], "gpflow.monitor.MonitorTask": [[26, 2, 1, "", "run"]], "gpflow.monitor.ScalarToTensorBoard": [[26, 2, 1, "", "run"]], "gpflow.optimizers": [[27, 1, 1, "", "NaturalGradient"], [27, 1, 1, "", "SamplingHelper"], [27, 1, 1, "", "Scipy"], [27, 1, 1, "", "XiNat"], [27, 1, 1, "", "XiSqrtMeanVar"], [27, 1, 1, "", "XiTransform"], [28, 0, 0, "-", "natgrad"]], "gpflow.optimizers.NaturalGradient": [[27, 2, 1, "", "get_config"], [27, 2, 1, "", "minimize"]], "gpflow.optimizers.SamplingHelper": [[27, 2, 1, "", "convert_to_constrained_values"], [27, 3, 1, "", "current_state"], [27, 3, 1, "", "target_log_prob_fn"]], "gpflow.optimizers.Scipy": [[27, 2, 1, "", "minimize"]], "gpflow.optimizers.XiNat": [[27, 2, 1, "", "meanvarsqrt_to_xi"], [27, 2, 1, "", "naturals_to_xi"], [27, 2, 1, "", "xi_to_meanvarsqrt"]], "gpflow.optimizers.XiSqrtMeanVar": [[27, 2, 1, "", "meanvarsqrt_to_xi"], [27, 2, 1, "", "naturals_to_xi"], [27, 2, 1, "", "xi_to_meanvarsqrt"]], "gpflow.optimizers.XiTransform": [[27, 2, 1, "", "meanvarsqrt_to_xi"], [27, 2, 1, "", "naturals_to_xi"], [27, 2, 1, "", "xi_to_meanvarsqrt"]], "gpflow.optimizers.natgrad": [[28, 4, 1, "", "expectation_to_meanvarsqrt"], [28, 4, 1, "", "expectation_to_natural"], [28, 4, 1, "", "meanvarsqrt_to_expectation"], [28, 4, 1, "", "meanvarsqrt_to_natural"], [28, 4, 1, "", "natural_to_expectation"], [28, 4, 1, "", "natural_to_meanvarsqrt"], [28, 4, 1, "", "swap_dimensions"]], "gpflow.posteriors": [[29, 1, 1, "", "AbstractPosterior"], [29, 1, 1, "", "BasePosterior"], [29, 1, 1, "", "FallbackIndependentLatentPosterior"], [29, 1, 1, "", "FullyCorrelatedPosterior"], [29, 1, 1, "", "GPRPosterior"], [29, 1, 1, "", "IndependentPosterior"], [29, 1, 1, "", "IndependentPosteriorMultiOutput"], [29, 1, 1, "", "IndependentPosteriorSingleOutput"], [29, 1, 1, "", "LinearCoregionalizationPosterior"], [29, 1, 1, "", "PrecomputeCacheType"], [29, 1, 1, "", "PrecomputedValue"], [29, 1, 1, "", "SGPRPosterior"], [29, 1, 1, "", "VGPPosterior"], [29, 4, 1, "", "_get_posterior_base_case"], [29, 4, 1, "", "_get_posterior_fully_correlated_mo"], [29, 4, 1, "", "_get_posterior_independent_mo"], [29, 4, 1, "", "_get_posterior_independentlatent_mo_fallback"], [29, 4, 1, "", "_get_posterior_linearcoregionalization_mo_efficient"], [29, 4, 1, "", "create_posterior"], [29, 4, 1, "", "get_precomputed_value_shape"]], "gpflow.posteriors.AbstractPosterior": [[29, 2, 1, "", "fused_predict_f"], [29, 2, 1, "", "predict_f"], [29, 2, 1, "", "update_cache"]], "gpflow.posteriors.PrecomputedValue": [[29, 5, 1, "", "axis_dynamic"], [29, 5, 1, "", "value"], [29, 2, 1, "", "wrap_alpha_Qinv"]], "gpflow.probability_distributions": [[30, 1, 1, "", "DiagonalGaussian"], [30, 1, 1, "", "Gaussian"], [30, 1, 1, "", "MarkovGaussian"], [30, 1, 1, "", "ProbabilityDistribution"], [30, 4, 1, "", "get_probability_distribution_shape"]], "gpflow.probability_distributions.DiagonalGaussian": [[30, 3, 1, "", "shape"]], "gpflow.probability_distributions.Gaussian": [[30, 3, 1, "", "shape"]], "gpflow.probability_distributions.MarkovGaussian": [[30, 3, 1, "", "shape"]], "gpflow.probability_distributions.ProbabilityDistribution": [[30, 3, 1, "", "shape"]], "gpflow.quadrature": [[32, 1, 1, "", "GaussianQuadrature"], [32, 1, 1, "", "NDiagGHQuadrature"], [31, 0, 0, "-", "gauss_hermite"], [32, 4, 1, "", "hermgauss"], [32, 4, 1, "", "mvhermgauss"], [32, 4, 1, "", "mvnquad"], [32, 4, 1, "", "ndiag_mc"], [32, 4, 1, "", "ndiagquad"]], "gpflow.quadrature.GaussianQuadrature": [[32, 2, 1, "", "logspace"]], "gpflow.quadrature.gauss_hermite": [[31, 4, 1, "", "gh_points_and_weights"], [31, 4, 1, "", "list_to_flat_grid"], [31, 4, 1, "", "ndgh_points_and_weights"], [31, 4, 1, "", "repeat_as_list"], [31, 4, 1, "", "reshape_Z_dZ"]], "gpflow.type_flags": [[33, 4, 1, "", "compute_mypy_flags"]], "gpflow.utilities": [[34, 1, 1, "", "Dispatcher"], [34, 4, 1, "", "add_likelihood_noise_cov"], [34, 4, 1, "", "add_noise_cov"], [34, 4, 1, "", "assert_params_false"], [34, 4, 1, "", "deepcopy"], [34, 4, 1, "", "freeze"], [34, 4, 1, "", "is_variable"], [34, 4, 1, "", "leaf_components"], [34, 4, 1, "", "multiple_assign"], [35, 0, 0, "-", "ops"], [34, 4, 1, "", "parameter_dict"], [36, 0, 0, "-", "parameter_or_function"], [34, 4, 1, "", "positive"], [34, 4, 1, "", "print_summary"], [34, 4, 1, "", "read_values"], [34, 4, 1, "", "reset_cache_bijectors"], [34, 4, 1, "", "select_dict_parameters_with_prior"], [34, 4, 1, "", "tabulate_module_summary"], [34, 4, 1, "", "to_default_float"], [34, 4, 1, "", "to_default_int"], [34, 4, 1, "", "training_loop"], [34, 4, 1, "", "traverse_module"], [34, 4, 1, "", "triangular"], [34, 4, 1, "", "triangular_size"]], "gpflow.utilities.Dispatcher": [[34, 2, 1, "", "dispatch"], [34, 2, 1, "", "dispatch_or_raise"], [34, 2, 1, "", "get_first_occurrence"], [34, 2, 1, "", "register"]], "gpflow.utilities.ops": [[35, 4, 1, "", "broadcasting_elementwise"], [35, 4, 1, "", "difference_matrix"], [35, 4, 1, "", "eye"], [35, 4, 1, "", "leading_transpose"], [35, 4, 1, "", "pca_reduce"], [35, 4, 1, "", "square_distance"]], "gpflow.utilities.parameter_or_function": [[36, 4, 1, "", "evaluate_parameter_or_function"], [36, 4, 1, "", "prepare_parameter_or_function"]]}, "objtypes": {"0": "py:module", "1": "py:class", "2": "py:method", "3": "py:property", "4": "py:function", "5": "py:attribute"}, "objnames": {"0": ["py", "module", "Python module"], "1": ["py", "class", "Python class"], "2": ["py", "method", "Python method"], "3": ["py", "property", "Python property"], "4": ["py", "function", "Python function"], "5": ["py", "attribute", "Python attribute"]}, "titleterms": {"gpflow": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 40, 51, 54, 65, 67], "base": [0, 13], "class": [0, 3, 9, 10, 11, 12, 13, 14, 16, 19, 20, 21, 22, 23, 25, 26, 27, 29, 30, 32, 34, 51, 62], "prioron": 0, "condit": [1, 2, 67], "modul": [1, 5, 7, 10, 11, 14, 16, 21, 27, 32, 34, 62], "function": [1, 2, 3, 4, 5, 6, 8, 9, 10, 15, 17, 18, 19, 21, 24, 25, 28, 29, 30, 31, 32, 33, 34, 35, 36, 55, 60, 64], "base_condit": 1, "sample_condit": 1, "uncertain_condit": 1, "util": [2, 8, 17, 24, 34, 35, 36], "base_conditional_with_lm": 2, "expand_independent_output": 2, "fully_correlated_condit": 2, "fully_correlated_conditional_repeat": 2, "independent_interdomain_condit": 2, "mix_latent_gp": 2, "rollaxis_left": 2, "rollaxis_right": 2, "sample_mvn": 2, "separate_independent_conditional_implement": 2, "config": 3, "as_context": 3, "default_positive_bijector": 3, "default_positive_minimum": 3, "default_summary_fmt": 3, "positive_bijector_type_map": 3, "set_config": 3, "set_default_float": 3, "set_default_int": 3, "set_default_jitt": 3, "set_default_positive_bijector": 3, "set_default_positive_minimum": 3, "set_default_summary_fmt": 3, "covari": [4, 56], "kuf": 4, "kuu": 4, "expect": [5, 6], "quadrature_expect": 5, "quadratur": [6, 31, 32], "get_eval_func": 6, "experiment": [7, 8], "addit": [9, 58], "constant": 9, "ident": 9, "linear": [9, 14], "meanfunct": 9, "polynomi": [9, 14, 55], "product": [9, 14], "switchedfunct": 9, "switchedmeanfunct": 9, "zero": 9, "paramet": [10, 49, 50, 52, 58, 62, 63], "default_float": 10, "default_int": 10, "default_jitt": 10, "set_train": 10, "inducing_vari": [11, 12], "fallbackseparateindependentinducingvari": 11, "fallbacksharedindependentinducingvari": 11, "inducingpatch": 11, "inducingpoint": 11, "inducingvari": 11, "multioutputinducingvari": 11, "multiscal": 11, "separateindependentinducingvari": 11, "sharedindependentinducingvari": 11, "inducingpointsbas": 12, "kernel": [13, 14, 44, 45, 48, 51, 52, 58, 60, 66], "reducingcombin": 13, "anisotropicstationari": 14, "arccosin": 14, "bia": 14, "changepoint": 14, "combin": [14, 51], "convolut": [14, 44, 65], "coregion": [14, 45], "cosin": 14, "exponenti": [14, 16, 18, 44, 49], "independentlat": 14, "isotropicstationari": 14, "linearcoregion": 14, "matern12": 14, "matern32": 14, "matern52": 14, "multioutputkernel": 14, "period": [14, 58], "rbf": 14, "rationalquadrat": 14, "separateindepend": 14, "sharedindepend": 14, "static": 14, "stationari": 14, "sum": 14, "white": 14, "kullback_leibl": 15, "gauss_kl": 15, "prior_kl": 15, "likelihood": [16, 17, 47, 48, 69, 72], "creat": [16, 55, 64], "new": 16, "bernoulli": [16, 18], "beta": [16, 18], "gamma": [16, 18], "gaussian": [16, 18, 30, 42, 44, 50, 51, 55, 57], "gaussianmc": 16, "heteroskedastictfpcondit": 16, "montecarlolikelihood": 16, "multiclass": [16, 49, 50], "multilatentlikelihood": 16, "multilatenttfpcondit": 16, "ordin": [16, 53], "poisson": [16, 18], "quadraturelikelihood": 16, "robustmax": 16, "scalarlikelihood": 16, "softmax": 16, "studentt": 16, "switchedlikelihood": 16, "inv_probit": 17, "logdens": 18, "laplac": 18, "lognorm": 18, "multivariate_norm": 18, "student_t": 18, "model": [19, 20, 21, 22, 23, 24, 25, 40, 42, 45, 47, 48, 49, 50, 51, 52, 55, 56, 57, 62, 63, 64, 65, 66, 67, 70, 72, 74], "cglb": [19, 21], "nystromprecondition": 19, "cglb_conjugate_gradi": 19, "gpr": [20, 21, 46, 52, 56], "gpr_deprec": 20, "gpr_with_posterior": 20, "bayesiangplvm": 21, "bayesianmodel": 21, "externaldatatraininglossmixin": 21, "gplvm": [21, 40, 42], "gpmc": 21, "gpmodel": 21, "gprfitc": 21, "internaldatatraininglossmixin": 21, "sgpmc": 21, "sgpr": [21, 22, 46, 59, 69], "svgp": [21, 23, 46, 47, 48, 50, 57], "vgp": [21, 25, 52, 57, 73], "vgpopperarchambeau": 21, "maximum_log_likelihood_object": 21, "training_loss": 21, "training_loss_closur": 21, "sgprbase_deprec": 22, "sgpr_deprec": 22, "sgpr_with_posterior": 22, "svgp_deprec": 23, "svgp_with_posterior": 23, "data_input_to_tensor": 24, "inducingpoint_wrapp": 24, "vgp_deprec": 25, "vgp_with_posterior": 25, "update_vgp_data": 25, "monitor": [26, 61], "executecallback": [26, 61], "imagetotensorboard": 26, "modeltotensorboard": 26, "monitortask": 26, "monitortaskgroup": 26, "scalartotensorboard": 26, "totensorboard": 26, "optim": [27, 28, 47, 48, 52, 73], "naturalgradi": 27, "samplinghelp": 27, "scipi": 27, "xinat": 27, "xisqrtmeanvar": 27, "xitransform": 27, "natgrad": [28, 48], "expectation_to_meanvarsqrt": 28, "expectation_to_natur": 28, "meanvarsqrt_to_expect": 28, "meanvarsqrt_to_natur": 28, "natural_to_expect": 28, "natural_to_meanvarsqrt": 28, "swap_dimens": 28, "posterior": [29, 46], "abstractposterior": 29, "baseposterior": 29, "fallbackindependentlatentposterior": 29, "fullycorrelatedposterior": 29, "gprposterior": 29, "independentposterior": 29, "independentposteriormultioutput": 29, "independentposteriorsingleoutput": 29, "linearcoregionalizationposterior": 29, "precomputecachetyp": 29, "precomputedvalu": 29, "sgprposterior": 29, "vgpposterior": 29, "create_posterior": 29, "get_posterior_class": 29, "get_precomputed_value_shap": 29, "probability_distribut": 30, "diagonalgaussian": 30, "markovgaussian": 30, "probabilitydistribut": 30, "get_probability_distribution_shap": 30, "gauss_hermit": 31, "gh_points_and_weight": 31, "list_to_flat_grid": 31, "ndgh_points_and_weight": 31, "repeat_as_list": 31, "reshape_z_dz": 31, "gaussianquadratur": 32, "ndiagghquadratur": 32, "hermgauss": 32, "mvhermgauss": 32, "mvnquad": 32, "ndiag_mc": 32, "ndiagquad": 32, "type_flag": 33, "compute_mypy_flag": 33, "dispatch": 34, "add_likelihood_noise_cov": 34, "add_noise_cov": 34, "assert_params_fals": 34, "deepcopi": 34, "freez": 34, "is_vari": 34, "leaf_compon": 34, "multiple_assign": 34, "parameter_dict": 34, "posit": 34, "print_summari": 34, "read_valu": 34, "reset_cache_bijector": 34, "select_dict_parameters_with_prior": 34, "tabulate_module_summari": 34, "to_default_float": 34, "to_default_int": 34, "training_loop": 34, "traverse_modul": 34, "triangular": 34, "triangular_s": 34, "op": 35, "broadcasting_elementwis": 35, "difference_matrix": 35, "ey": 35, "leading_transpos": 35, "pca_reduc": 35, "square_dist": 35, "parameter_or_funct": 36, "evaluate_parameter_or_funct": 36, "prepare_parameter_or_funct": 36, "benchmark": 37, "bibliographi": 38, "get": 39, "start": 39, "document": 40, "what": [40, 46, 56, 58, 62], "ar": 40, "implement": [40, 51, 67], "regress": [40, 48, 49, 53, 55, 57], "mcmc": [40, 49], "variat": [40, 47, 50, 52, 54, 57, 72], "infer": [40, 47, 49, 50, 51], "interdomain": 40, "multioutput": 40, "gp": [40, 48, 49, 50, 64, 72], "heteroskedast": [40, 48], "contact": 40, "cite": 40, "acknowledg": 40, "instal": 41, "pre": 41, "built": 41, "from": [41, 50], "sourc": 41, "version": 41, "bayesian": [42, 49], "process": [42, 44, 50, 51, 55, 57], "latent": [42, 48], "variabl": [42, 51], "data": [42, 45, 47, 48, 49, 50, 51, 55, 57, 58, 59], "construct": [42, 45], "analysi": 42, "plot": [42, 48, 50, 56], "v": [42, 47, 56], "principl": 42, "compon": [42, 61], "pca": 42, "refer": [42, 45, 47, 64, 67, 69], "chang": [43, 58], "point": [43, 48, 51, 58, 59], "gener": [44, 47, 48, 49, 50, 51, 55, 64], "dataset": [44, 62, 67], "squar": 44, "conclus": 44, "A": [45, 67, 72], "simpl": [45, 58], "demonstr": 45, "prepar": 45, "format": 45, "build": [45, 47, 48, 64], "faster": 46, "predict": [46, 69, 73], "cach": 46, "distribut": [46, 57, 73], "can": 46, "exampl": [46, 49], "stochast": 47, "scalabl": 47, "comput": 47, "batch": 47, "minibatch": [47, 52], "estim": [47, 67, 72], "elbo": 47, "speed": 47, "up": 47, "run": [47, 48, 50], "further": [47, 48, 51, 55], "read": [47, 48, 51, 55], "multi": [48, 51, 58, 62], "standard": 48, "homoskedast": 48, "induc": [48, 51, 59], "adam": 48, "loop": 48, "markov": 49, "chain": 49, "mont": 49, "carlo": 49, "1": [49, 51, 55, 67], "one": 49, "dimension": [49, 58], "problem": 49, "hyperparamet": [49, 52, 72], "theta": 49, "2": [49, 51, 55, 67], "spars": [49, 50, 52, 57, 72], "mc": 49, "classif": [49, 50, 52, 57], "3": [49, 51, 55], "fulli": 49, "hmc": 49, "prior": [49, 62], "constrain": 49, "unconstrain": 49, "sampl": [50, 59], "declar": 50, "input": 50, "approxim": [50, 68], "see": [50, 66], "big": 50, "output": [51, 55], "task": [51, 64], "synthet": 51, "f": [51, 56, 73], "x": 51, "directli": 51, "share": 51, "independ": 51, "mok": 51, "separ": 51, "do": [51, 62], "g": 51, "space": 51, "mix": [51, 65], "uncorrel": [51, 59], "illustr": 51, "": [51, 56], "capabl": 51, "diagram": 51, "fallback": 51, "debug": 51, "introspect": 51, "natur": 52, "gradient": [52, 71], "i": [52, 58], "both": [52, 57], "togeth": 52, "also": [52, 66], "work": 52, "comparison": 52, "ordinari": 52, "conjug": [52, 71], "case": 52, "non": [52, 57], "binari": 52, "fourier": 54, "featur": 54, "framework": 54, "vari": 55, "nois": 55, "demo": 55, "known": 55, "varianc": [55, 56], "try": 55, "naiv": 55, "fit": [55, 62], "scale": 55, "group": 55, "structur": 55, "us": [55, 63, 66], "multipl": [55, 58], "empir": 55, "custom": [55, 60, 64], "basic": 56, "usag": 56, "import": 56, "meet": 56, "y": 56, "minim": 56, "margin": [56, 69, 72, 73], "full": [56, 72], "next": 56, "other": [57, 58], "The": [57, 58, 62, 67], "gaussion": 57, "write": 57, "code": 57, "handl": 57, "intern": 57, "extern": 57, "visualis": 58, "mat\u00e9rn": 58, "famili": 58, "composit": [58, 60], "some": 58, "activ": 58, "dimens": 58, "larg": 59, "pick": 59, "initi": [59, 62], "random": 59, "k": [59, 66], "mean": [59, 60, 64], "advanc": [59, 62, 74], "initialis": 59, "revers": 60, "set": [60, 62], "interact": 60, "versu": 60, "tensorboard": 61, "integr": 61, "Their": 62, "optimis": 62, "inspect": 62, "you": 62, "fail": 62, "co_2": 62, "level": 62, "valu": [62, 63], "transform": 62, "trainabl": 62, "train": 62, "stage": 62, "kera": 62, "save": 63, "load": 63, "checkpoint": 63, "tensorflow": [63, 65], "saved_model": 63, "copi": 63, "hyper": 63, "between": 63, "which": 63, "method": 63, "metalearn": 64, "metamodel": 64, "assess": 64, "network": [65, 67], "insid": 65, "design": 66, "__init__": 66, "k_diag": 66, "mixtur": 67, "densiti": 67, "mdn": 67, "note": [67, 74], "experi": 67, "sinusoid": 67, "half": 67, "moon": 67, "compar": 68, "fitc": 68, "vfe": 68, "deriv": [69, 73], "equat": [69, 73], "bound": [69, 71, 72], "saniti": 70, "check": 70, "when": 70, "behaviour": 70, "should": 70, "overlap": 70, "lower": 71, "discuss": 72, "upper": 72, "fix": 72, "tight": 72, "doe": 72, "impli": 72, "converg": 72, "q": 73, "mathbf": 73, "kl": 73, "diverg": 73, "user": 74, "guid": 74, "theoret": 74, "tailor": 74, "need": 74}, "envversion": {"sphinx.domains.c": 2, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 8, "sphinx.domains.index": 1, "sphinx.domains.javascript": 2, "sphinx.domains.math": 2, "sphinx.domains.python": 3, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.todo": 2, "sphinx.ext.viewcode": 1, "sphinxcontrib.bibtex": 9, "nbsphinx": 4, "sphinx": 57}, "alltitles": {"gpflow.base": [[0, "gpflow-base"]], "Classes": [[0, "classes"], [3, "classes"], [9, "classes"], [10, "classes"], [11, "classes"], [12, "classes"], [13, "classes"], [14, "classes"], [16, "classes"], [19, "classes"], [20, "classes"], [21, "classes"], [22, "classes"], [23, "classes"], [25, "classes"], [26, "classes"], [27, "classes"], [29, "classes"], [30, "classes"], [32, "classes"], [34, "classes"]], "gpflow.base.PriorOn": [[0, "gpflow-base-prioron"]], "gpflow.conditionals": [[1, "gpflow-conditionals"]], "Modules": [[1, "modules"], [5, "modules"], [7, "modules"], [10, "modules"], [11, "modules"], [14, "modules"], [16, "modules"], [21, "modules"], [27, "modules"], [32, "modules"], [34, "modules"]], "Functions": [[1, "functions"], [2, "functions"], [3, "functions"], [4, "functions"], [5, "functions"], [6, "functions"], [8, "functions"], [10, "functions"], [15, "functions"], [17, "functions"], [18, "functions"], [19, "functions"], [21, "functions"], [24, "functions"], [25, "functions"], [28, "functions"], [29, "functions"], [30, "functions"], [31, "functions"], [32, "functions"], [33, "functions"], [34, "functions"], [35, "functions"], [36, "functions"]], "gpflow.conditionals.base_conditional": [[1, "gpflow-conditionals-base-conditional"]], "gpflow.conditionals.conditional": [[1, "gpflow-conditionals-conditional"]], "gpflow.conditionals.sample_conditional": [[1, "gpflow-conditionals-sample-conditional"]], "gpflow.conditionals.uncertain_conditional": [[1, "gpflow-conditionals-uncertain-conditional"]], "gpflow.conditionals.util": [[2, "gpflow-conditionals-util"]], "gpflow.conditionals.util.base_conditional_with_lm": [[2, "gpflow-conditionals-util-base-conditional-with-lm"]], "gpflow.conditionals.util.expand_independent_outputs": [[2, "gpflow-conditionals-util-expand-independent-outputs"]], "gpflow.conditionals.util.fully_correlated_conditional": [[2, "gpflow-conditionals-util-fully-correlated-conditional"]], "gpflow.conditionals.util.fully_correlated_conditional_repeat": [[2, "gpflow-conditionals-util-fully-correlated-conditional-repeat"]], "gpflow.conditionals.util.independent_interdomain_conditional": [[2, "gpflow-conditionals-util-independent-interdomain-conditional"]], "gpflow.conditionals.util.mix_latent_gp": [[2, "gpflow-conditionals-util-mix-latent-gp"]], "gpflow.conditionals.util.rollaxis_left": [[2, "gpflow-conditionals-util-rollaxis-left"]], "gpflow.conditionals.util.rollaxis_right": [[2, "gpflow-conditionals-util-rollaxis-right"]], "gpflow.conditionals.util.sample_mvn": [[2, "gpflow-conditionals-util-sample-mvn"]], "gpflow.conditionals.util.separate_independent_conditional_implementation": [[2, "gpflow-conditionals-util-separate-independent-conditional-implementation"]], "gpflow.config": [[3, "gpflow-config"]], "gpflow.config.Config": [[3, "gpflow-config-config"]], "gpflow.config.as_context": [[3, "gpflow-config-as-context"]], "gpflow.config.config": [[3, "id1"]], "gpflow.config.default_positive_bijector": [[3, "gpflow-config-default-positive-bijector"]], "gpflow.config.default_positive_minimum": [[3, "gpflow-config-default-positive-minimum"]], "gpflow.config.default_summary_fmt": [[3, "gpflow-config-default-summary-fmt"]], "gpflow.config.positive_bijector_type_map": [[3, "gpflow-config-positive-bijector-type-map"]], "gpflow.config.set_config": [[3, "gpflow-config-set-config"]], "gpflow.config.set_default_float": [[3, "gpflow-config-set-default-float"]], "gpflow.config.set_default_int": [[3, "gpflow-config-set-default-int"]], "gpflow.config.set_default_jitter": [[3, "gpflow-config-set-default-jitter"]], "gpflow.config.set_default_positive_bijector": [[3, "gpflow-config-set-default-positive-bijector"]], "gpflow.config.set_default_positive_minimum": [[3, "gpflow-config-set-default-positive-minimum"]], "gpflow.config.set_default_summary_fmt": [[3, "gpflow-config-set-default-summary-fmt"]], "gpflow.covariances": [[4, "gpflow-covariances"]], "gpflow.covariances.Kuf": [[4, "gpflow-covariances-kuf"]], "gpflow.covariances.Kuu": [[4, "gpflow-covariances-kuu"]], "gpflow.expectations": [[5, "gpflow-expectations"]], "gpflow.expectations.expectation": [[5, "gpflow-expectations-expectation"]], "gpflow.expectations.quadrature_expectation": [[5, "gpflow-expectations-quadrature-expectation"]], "gpflow.expectations.quadratures": [[6, "gpflow-expectations-quadratures"]], "gpflow.expectations.quadratures.get_eval_func": [[6, "gpflow-expectations-quadratures-get-eval-func"]], "gpflow.experimental": [[7, "gpflow-experimental"]], "gpflow.experimental.utils": [[8, "gpflow-experimental-utils"]], "gpflow.experimental.utils.experimental": [[8, "gpflow-experimental-utils-experimental"]], "gpflow.functions": [[9, "gpflow-functions"]], "gpflow.functions.Additive": [[9, "gpflow-functions-additive"]], "gpflow.functions.Constant": [[9, "gpflow-functions-constant"]], "gpflow.functions.Function": [[9, "gpflow-functions-function"]], "gpflow.functions.Identity": [[9, "gpflow-functions-identity"]], "gpflow.functions.Linear": [[9, "gpflow-functions-linear"]], "gpflow.functions.MeanFunction": [[9, "gpflow-functions-meanfunction"]], "gpflow.functions.Polynomial": [[9, "gpflow-functions-polynomial"]], "gpflow.functions.Product": [[9, "gpflow-functions-product"]], "gpflow.functions.SwitchedFunction": [[9, "gpflow-functions-switchedfunction"]], "gpflow.functions.SwitchedMeanFunction": [[9, "gpflow-functions-switchedmeanfunction"]], "gpflow.functions.Zero": [[9, "gpflow-functions-zero"]], "gpflow": [[10, "gpflow"]], "gpflow.Module": [[10, "gpflow-module"]], "gpflow.Parameter": [[10, "gpflow-parameter"]], "gpflow.default_float": [[10, "gpflow-default-float"]], "gpflow.default_int": [[10, "gpflow-default-int"]], "gpflow.default_jitter": [[10, "gpflow-default-jitter"]], "gpflow.set_trainable": [[10, "gpflow-set-trainable"]], "gpflow.inducing_variables": [[11, "gpflow-inducing-variables"]], "gpflow.inducing_variables.FallbackSeparateIndependentInducingVariables": [[11, "gpflow-inducing-variables-fallbackseparateindependentinducingvariables"]], "gpflow.inducing_variables.FallbackSharedIndependentInducingVariables": [[11, "gpflow-inducing-variables-fallbacksharedindependentinducingvariables"]], "gpflow.inducing_variables.InducingPatches": [[11, "gpflow-inducing-variables-inducingpatches"]], "gpflow.inducing_variables.InducingPoints": [[11, "gpflow-inducing-variables-inducingpoints"]], "gpflow.inducing_variables.InducingVariables": [[11, "gpflow-inducing-variables-inducingvariables"]], "gpflow.inducing_variables.MultioutputInducingVariables": [[11, "gpflow-inducing-variables-multioutputinducingvariables"]], "gpflow.inducing_variables.Multiscale": [[11, "gpflow-inducing-variables-multiscale"]], "gpflow.inducing_variables.SeparateIndependentInducingVariables": [[11, "gpflow-inducing-variables-separateindependentinducingvariables"]], "gpflow.inducing_variables.SharedIndependentInducingVariables": [[11, "gpflow-inducing-variables-sharedindependentinducingvariables"]], "gpflow.inducing_variables.inducing_variables": [[12, "gpflow-inducing-variables-inducing-variables"]], "gpflow.inducing_variables.inducing_variables.InducingPointsBase": [[12, "gpflow-inducing-variables-inducing-variables-inducingpointsbase"]], "gpflow.kernels.base": [[13, "gpflow-kernels-base"]], "gpflow.kernels.base.ReducingCombination": [[13, "gpflow-kernels-base-reducingcombination"]], "gpflow.kernels": [[14, "gpflow-kernels"]], "gpflow.kernels.AnisotropicStationary": [[14, "gpflow-kernels-anisotropicstationary"]], "gpflow.kernels.ArcCosine": [[14, "gpflow-kernels-arccosine"]], "gpflow.kernels.Bias": [[14, "gpflow-kernels-bias"]], "gpflow.kernels.ChangePoints": [[14, "gpflow-kernels-changepoints"]], "gpflow.kernels.Combination": [[14, "gpflow-kernels-combination"]], "gpflow.kernels.Convolutional": [[14, "gpflow-kernels-convolutional"]], "gpflow.kernels.Coregion": [[14, "gpflow-kernels-coregion"]], "gpflow.kernels.Cosine": [[14, "gpflow-kernels-cosine"]], "gpflow.kernels.Exponential": [[14, "gpflow-kernels-exponential"]], "gpflow.kernels.IndependentLatent": [[14, "gpflow-kernels-independentlatent"]], "gpflow.kernels.IsotropicStationary": [[14, "gpflow-kernels-isotropicstationary"]], "gpflow.kernels.Kernel": [[14, "gpflow-kernels-kernel"]], "gpflow.kernels.Linear": [[14, "gpflow-kernels-linear"]], "gpflow.kernels.LinearCoregionalization": [[14, "gpflow-kernels-linearcoregionalization"]], "gpflow.kernels.Matern12": [[14, "gpflow-kernels-matern12"]], "gpflow.kernels.Matern32": [[14, "gpflow-kernels-matern32"]], "gpflow.kernels.Matern52": [[14, "gpflow-kernels-matern52"]], "gpflow.kernels.MultioutputKernel": [[14, "gpflow-kernels-multioutputkernel"]], "gpflow.kernels.Periodic": [[14, "gpflow-kernels-periodic"]], "gpflow.kernels.Polynomial": [[14, "gpflow-kernels-polynomial"]], "gpflow.kernels.Product": [[14, "gpflow-kernels-product"]], "gpflow.kernels.RBF": [[14, "gpflow-kernels-rbf"]], "gpflow.kernels.RationalQuadratic": [[14, "gpflow-kernels-rationalquadratic"]], "gpflow.kernels.SeparateIndependent": [[14, "gpflow-kernels-separateindependent"]], "gpflow.kernels.SharedIndependent": [[14, "gpflow-kernels-sharedindependent"]], "gpflow.kernels.Static": [[14, "gpflow-kernels-static"]], "gpflow.kernels.Stationary": [[14, "gpflow-kernels-stationary"]], "gpflow.kernels.Sum": [[14, "gpflow-kernels-sum"]], "gpflow.kernels.White": [[14, "gpflow-kernels-white"]], "gpflow.kullback_leiblers": [[15, "gpflow-kullback-leiblers"]], "gpflow.kullback_leiblers.gauss_kl": [[15, "gpflow-kullback-leiblers-gauss-kl"]], "gpflow.kullback_leiblers.prior_kl": [[15, "gpflow-kullback-leiblers-prior-kl"]], "gpflow.likelihoods": [[16, "gpflow-likelihoods"]], "Creating new likelihoods": [[16, "creating-new-likelihoods"]], "gpflow.likelihoods.Bernoulli": [[16, "gpflow-likelihoods-bernoulli"]], "gpflow.likelihoods.Beta": [[16, "gpflow-likelihoods-beta"]], "gpflow.likelihoods.Exponential": [[16, "gpflow-likelihoods-exponential"]], "gpflow.likelihoods.Gamma": [[16, "gpflow-likelihoods-gamma"]], "gpflow.likelihoods.Gaussian": [[16, "gpflow-likelihoods-gaussian"]], "gpflow.likelihoods.GaussianMC": [[16, "gpflow-likelihoods-gaussianmc"]], "gpflow.likelihoods.HeteroskedasticTFPConditional": [[16, "gpflow-likelihoods-heteroskedastictfpconditional"]], "gpflow.likelihoods.Likelihood": [[16, "gpflow-likelihoods-likelihood"]], "gpflow.likelihoods.MonteCarloLikelihood": [[16, "gpflow-likelihoods-montecarlolikelihood"]], "gpflow.likelihoods.MultiClass": [[16, "gpflow-likelihoods-multiclass"]], "gpflow.likelihoods.MultiLatentLikelihood": [[16, "gpflow-likelihoods-multilatentlikelihood"]], "gpflow.likelihoods.MultiLatentTFPConditional": [[16, "gpflow-likelihoods-multilatenttfpconditional"]], "gpflow.likelihoods.Ordinal": [[16, "gpflow-likelihoods-ordinal"]], "gpflow.likelihoods.Poisson": [[16, "gpflow-likelihoods-poisson"]], "gpflow.likelihoods.QuadratureLikelihood": [[16, "gpflow-likelihoods-quadraturelikelihood"]], "gpflow.likelihoods.RobustMax": [[16, "gpflow-likelihoods-robustmax"]], "gpflow.likelihoods.ScalarLikelihood": [[16, "gpflow-likelihoods-scalarlikelihood"]], "gpflow.likelihoods.Softmax": [[16, "gpflow-likelihoods-softmax"]], "gpflow.likelihoods.StudentT": [[16, "gpflow-likelihoods-studentt"]], "gpflow.likelihoods.SwitchedLikelihood": [[16, "gpflow-likelihoods-switchedlikelihood"]], "gpflow.likelihoods.utils": [[17, "gpflow-likelihoods-utils"]], "gpflow.likelihoods.utils.inv_probit": [[17, "gpflow-likelihoods-utils-inv-probit"]], "gpflow.logdensities": [[18, "gpflow-logdensities"]], "gpflow.logdensities.bernoulli": [[18, "gpflow-logdensities-bernoulli"]], "gpflow.logdensities.beta": [[18, "gpflow-logdensities-beta"]], "gpflow.logdensities.exponential": [[18, "gpflow-logdensities-exponential"]], "gpflow.logdensities.gamma": [[18, "gpflow-logdensities-gamma"]], "gpflow.logdensities.gaussian": [[18, "gpflow-logdensities-gaussian"]], "gpflow.logdensities.laplace": [[18, "gpflow-logdensities-laplace"]], "gpflow.logdensities.lognormal": [[18, "gpflow-logdensities-lognormal"]], "gpflow.logdensities.multivariate_normal": [[18, "gpflow-logdensities-multivariate-normal"]], "gpflow.logdensities.poisson": [[18, "gpflow-logdensities-poisson"]], "gpflow.logdensities.student_t": [[18, "gpflow-logdensities-student-t"]], "gpflow.models.cglb": [[19, "gpflow-models-cglb"]], "gpflow.models.cglb.NystromPreconditioner": [[19, "gpflow-models-cglb-nystrompreconditioner"]], "gpflow.models.cglb.cglb_conjugate_gradient": [[19, "gpflow-models-cglb-cglb-conjugate-gradient"]], "gpflow.models.gpr": [[20, "gpflow-models-gpr"]], "gpflow.models.gpr.GPR_deprecated": [[20, "gpflow-models-gpr-gpr-deprecated"]], "gpflow.models.gpr.GPR_with_posterior": [[20, "gpflow-models-gpr-gpr-with-posterior"]], "gpflow.models": [[21, "gpflow-models"]], "gpflow.models.BayesianGPLVM": [[21, "gpflow-models-bayesiangplvm"]], "gpflow.models.BayesianModel": [[21, "gpflow-models-bayesianmodel"]], "gpflow.models.CGLB": [[21, "gpflow-models-cglb"]], "gpflow.models.ExternalDataTrainingLossMixin": [[21, "gpflow-models-externaldatatraininglossmixin"]], "gpflow.models.GPLVM": [[21, "gpflow-models-gplvm"]], "gpflow.models.GPMC": [[21, "gpflow-models-gpmc"]], "gpflow.models.GPModel": [[21, "gpflow-models-gpmodel"]], "gpflow.models.GPR": [[21, "gpflow-models-gpr"]], "gpflow.models.GPRFITC": [[21, "gpflow-models-gprfitc"]], "gpflow.models.InternalDataTrainingLossMixin": [[21, "gpflow-models-internaldatatraininglossmixin"]], "gpflow.models.SGPMC": [[21, "gpflow-models-sgpmc"]], "gpflow.models.SGPR": [[21, "gpflow-models-sgpr"]], "gpflow.models.SVGP": [[21, "gpflow-models-svgp"]], "gpflow.models.VGP": [[21, "gpflow-models-vgp"]], "gpflow.models.VGPOpperArchambeau": [[21, "gpflow-models-vgpopperarchambeau"]], "gpflow.models.maximum_log_likelihood_objective": [[21, "gpflow-models-maximum-log-likelihood-objective"]], "gpflow.models.training_loss": [[21, "gpflow-models-training-loss"]], "gpflow.models.training_loss_closure": [[21, "gpflow-models-training-loss-closure"]], "gpflow.models.sgpr": [[22, "gpflow-models-sgpr"]], "gpflow.models.sgpr.SGPRBase_deprecated": [[22, "gpflow-models-sgpr-sgprbase-deprecated"]], "gpflow.models.sgpr.SGPR_deprecated": [[22, "gpflow-models-sgpr-sgpr-deprecated"]], "gpflow.models.sgpr.SGPR_with_posterior": [[22, "gpflow-models-sgpr-sgpr-with-posterior"]], "gpflow.models.svgp": [[23, "gpflow-models-svgp"]], "gpflow.models.svgp.SVGP_deprecated": [[23, "gpflow-models-svgp-svgp-deprecated"]], "gpflow.models.svgp.SVGP_with_posterior": [[23, "gpflow-models-svgp-svgp-with-posterior"]], "gpflow.models.util": [[24, "gpflow-models-util"]], "gpflow.models.util.data_input_to_tensor": [[24, "gpflow-models-util-data-input-to-tensor"]], "gpflow.models.util.inducingpoint_wrapper": [[24, "gpflow-models-util-inducingpoint-wrapper"]], "gpflow.models.vgp": [[25, "gpflow-models-vgp"]], "gpflow.models.vgp.VGP_deprecated": [[25, "gpflow-models-vgp-vgp-deprecated"]], "gpflow.models.vgp.VGP_with_posterior": [[25, "gpflow-models-vgp-vgp-with-posterior"]], "gpflow.models.vgp.update_vgp_data": [[25, "gpflow-models-vgp-update-vgp-data"]], "gpflow.monitor": [[26, "gpflow-monitor"]], "gpflow.monitor.ExecuteCallback": [[26, "gpflow-monitor-executecallback"]], "gpflow.monitor.ImageToTensorBoard": [[26, "gpflow-monitor-imagetotensorboard"]], "gpflow.monitor.ModelToTensorBoard": [[26, "gpflow-monitor-modeltotensorboard"]], "gpflow.monitor.Monitor": [[26, "gpflow-monitor-monitor"]], "gpflow.monitor.MonitorTask": [[26, "gpflow-monitor-monitortask"]], "gpflow.monitor.MonitorTaskGroup": [[26, "gpflow-monitor-monitortaskgroup"]], "gpflow.monitor.ScalarToTensorBoard": [[26, "gpflow-monitor-scalartotensorboard"]], "gpflow.monitor.ToTensorBoard": [[26, "gpflow-monitor-totensorboard"]], "gpflow.optimizers": [[27, "gpflow-optimizers"]], "gpflow.optimizers.NaturalGradient": [[27, "gpflow-optimizers-naturalgradient"]], "gpflow.optimizers.SamplingHelper": [[27, "gpflow-optimizers-samplinghelper"]], "gpflow.optimizers.Scipy": [[27, "gpflow-optimizers-scipy"]], "gpflow.optimizers.XiNat": [[27, "gpflow-optimizers-xinat"]], "gpflow.optimizers.XiSqrtMeanVar": [[27, "gpflow-optimizers-xisqrtmeanvar"]], "gpflow.optimizers.XiTransform": [[27, "gpflow-optimizers-xitransform"]], "gpflow.optimizers.natgrad": [[28, "gpflow-optimizers-natgrad"]], "gpflow.optimizers.natgrad.expectation_to_meanvarsqrt": [[28, "gpflow-optimizers-natgrad-expectation-to-meanvarsqrt"]], "gpflow.optimizers.natgrad.expectation_to_natural": [[28, "gpflow-optimizers-natgrad-expectation-to-natural"]], "gpflow.optimizers.natgrad.meanvarsqrt_to_expectation": [[28, "gpflow-optimizers-natgrad-meanvarsqrt-to-expectation"]], "gpflow.optimizers.natgrad.meanvarsqrt_to_natural": [[28, "gpflow-optimizers-natgrad-meanvarsqrt-to-natural"]], "gpflow.optimizers.natgrad.natural_to_expectation": [[28, "gpflow-optimizers-natgrad-natural-to-expectation"]], "gpflow.optimizers.natgrad.natural_to_meanvarsqrt": [[28, "gpflow-optimizers-natgrad-natural-to-meanvarsqrt"]], "gpflow.optimizers.natgrad.swap_dimensions": [[28, "gpflow-optimizers-natgrad-swap-dimensions"]], "gpflow.posteriors": [[29, "gpflow-posteriors"]], "gpflow.posteriors.AbstractPosterior": [[29, "gpflow-posteriors-abstractposterior"]], "gpflow.posteriors.BasePosterior": [[29, "gpflow-posteriors-baseposterior"]], "gpflow.posteriors.FallbackIndependentLatentPosterior": [[29, "gpflow-posteriors-fallbackindependentlatentposterior"]], "gpflow.posteriors.FullyCorrelatedPosterior": [[29, "gpflow-posteriors-fullycorrelatedposterior"]], "gpflow.posteriors.GPRPosterior": [[29, "gpflow-posteriors-gprposterior"]], "gpflow.posteriors.IndependentPosterior": [[29, "gpflow-posteriors-independentposterior"]], "gpflow.posteriors.IndependentPosteriorMultiOutput": [[29, "gpflow-posteriors-independentposteriormultioutput"]], "gpflow.posteriors.IndependentPosteriorSingleOutput": [[29, "gpflow-posteriors-independentposteriorsingleoutput"]], "gpflow.posteriors.LinearCoregionalizationPosterior": [[29, "gpflow-posteriors-linearcoregionalizationposterior"]], "gpflow.posteriors.PrecomputeCacheType": [[29, "gpflow-posteriors-precomputecachetype"]], "gpflow.posteriors.PrecomputedValue": [[29, "gpflow-posteriors-precomputedvalue"]], "gpflow.posteriors.SGPRPosterior": [[29, "gpflow-posteriors-sgprposterior"]], "gpflow.posteriors.VGPPosterior": [[29, "gpflow-posteriors-vgpposterior"]], "gpflow.posteriors.create_posterior": [[29, "gpflow-posteriors-create-posterior"]], "gpflow.posteriors.get_posterior_class": [[29, "gpflow-posteriors-get-posterior-class"]], "gpflow.posteriors.get_precomputed_value_shape": [[29, "gpflow-posteriors-get-precomputed-value-shape"]], "gpflow.probability_distributions": [[30, "gpflow-probability-distributions"]], "gpflow.probability_distributions.DiagonalGaussian": [[30, "gpflow-probability-distributions-diagonalgaussian"]], "gpflow.probability_distributions.Gaussian": [[30, "gpflow-probability-distributions-gaussian"]], "gpflow.probability_distributions.MarkovGaussian": [[30, "gpflow-probability-distributions-markovgaussian"]], "gpflow.probability_distributions.ProbabilityDistribution": [[30, "gpflow-probability-distributions-probabilitydistribution"]], "gpflow.probability_distributions.get_probability_distribution_shape": [[30, "gpflow-probability-distributions-get-probability-distribution-shape"]], "gpflow.quadrature.gauss_hermite": [[31, "gpflow-quadrature-gauss-hermite"]], "gpflow.quadrature.gauss_hermite.gh_points_and_weights": [[31, "gpflow-quadrature-gauss-hermite-gh-points-and-weights"]], "gpflow.quadrature.gauss_hermite.list_to_flat_grid": [[31, "gpflow-quadrature-gauss-hermite-list-to-flat-grid"]], "gpflow.quadrature.gauss_hermite.ndgh_points_and_weights": [[31, "gpflow-quadrature-gauss-hermite-ndgh-points-and-weights"]], "gpflow.quadrature.gauss_hermite.repeat_as_list": [[31, "gpflow-quadrature-gauss-hermite-repeat-as-list"]], "gpflow.quadrature.gauss_hermite.reshape_Z_dZ": [[31, "gpflow-quadrature-gauss-hermite-reshape-z-dz"]], "gpflow.quadrature": [[32, "gpflow-quadrature"]], "gpflow.quadrature.GaussianQuadrature": [[32, "gpflow-quadrature-gaussianquadrature"]], "gpflow.quadrature.NDiagGHQuadrature": [[32, "gpflow-quadrature-ndiagghquadrature"]], "gpflow.quadrature.hermgauss": [[32, "gpflow-quadrature-hermgauss"]], "gpflow.quadrature.mvhermgauss": [[32, "gpflow-quadrature-mvhermgauss"]], "gpflow.quadrature.mvnquad": [[32, "gpflow-quadrature-mvnquad"]], "gpflow.quadrature.ndiag_mc": [[32, "gpflow-quadrature-ndiag-mc"]], "gpflow.quadrature.ndiagquad": [[32, "gpflow-quadrature-ndiagquad"]], "gpflow.type_flags": [[33, "gpflow-type-flags"]], "gpflow.type_flags.compute_mypy_flags": [[33, "gpflow-type-flags-compute-mypy-flags"]], "gpflow.utilities": [[34, "gpflow-utilities"]], "gpflow.utilities.Dispatcher": [[34, "gpflow-utilities-dispatcher"]], "gpflow.utilities.add_likelihood_noise_cov": [[34, "gpflow-utilities-add-likelihood-noise-cov"]], "gpflow.utilities.add_noise_cov": [[34, "gpflow-utilities-add-noise-cov"]], "gpflow.utilities.assert_params_false": [[34, "gpflow-utilities-assert-params-false"]], "gpflow.utilities.deepcopy": [[34, "gpflow-utilities-deepcopy"]], "gpflow.utilities.freeze": [[34, "gpflow-utilities-freeze"]], "gpflow.utilities.is_variable": [[34, "gpflow-utilities-is-variable"]], "gpflow.utilities.leaf_components": [[34, "gpflow-utilities-leaf-components"]], "gpflow.utilities.multiple_assign": [[34, "gpflow-utilities-multiple-assign"]], "gpflow.utilities.parameter_dict": [[34, "gpflow-utilities-parameter-dict"]], "gpflow.utilities.positive": [[34, "gpflow-utilities-positive"]], "gpflow.utilities.print_summary": [[34, "gpflow-utilities-print-summary"]], "gpflow.utilities.read_values": [[34, "gpflow-utilities-read-values"]], "gpflow.utilities.reset_cache_bijectors": [[34, "gpflow-utilities-reset-cache-bijectors"]], "gpflow.utilities.select_dict_parameters_with_prior": [[34, "gpflow-utilities-select-dict-parameters-with-prior"]], "gpflow.utilities.tabulate_module_summary": [[34, "gpflow-utilities-tabulate-module-summary"]], "gpflow.utilities.to_default_float": [[34, "gpflow-utilities-to-default-float"]], "gpflow.utilities.to_default_int": [[34, "gpflow-utilities-to-default-int"]], "gpflow.utilities.training_loop": [[34, "gpflow-utilities-training-loop"]], "gpflow.utilities.traverse_module": [[34, "gpflow-utilities-traverse-module"]], "gpflow.utilities.triangular": [[34, "gpflow-utilities-triangular"]], "gpflow.utilities.triangular_size": [[34, "gpflow-utilities-triangular-size"]], "gpflow.utilities.ops": [[35, "gpflow-utilities-ops"]], "gpflow.utilities.ops.broadcasting_elementwise": [[35, "gpflow-utilities-ops-broadcasting-elementwise"]], "gpflow.utilities.ops.difference_matrix": [[35, "gpflow-utilities-ops-difference-matrix"]], "gpflow.utilities.ops.eye": [[35, "gpflow-utilities-ops-eye"]], "gpflow.utilities.ops.leading_transpose": [[35, "gpflow-utilities-ops-leading-transpose"]], "gpflow.utilities.ops.pca_reduce": [[35, "gpflow-utilities-ops-pca-reduce"]], "gpflow.utilities.ops.square_distance": [[35, "gpflow-utilities-ops-square-distance"]], "gpflow.utilities.parameter_or_function": [[36, "gpflow-utilities-parameter-or-function"]], "gpflow.utilities.parameter_or_function.evaluate_parameter_or_function": [[36, "gpflow-utilities-parameter-or-function-evaluate-parameter-or-function"]], "gpflow.utilities.parameter_or_function.prepare_parameter_or_function": [[36, "gpflow-utilities-parameter-or-function-prepare-parameter-or-function"]], "Benchmarks": [[37, "benchmarks"]], "Bibliography": [[38, "bibliography"]], "Getting Started": [[39, "getting-started"]], "GPflow": [[40, "gpflow"]], "Documentation": [[40, "documentation"]], "What models are implemented?": [[40, "what-models-are-implemented"]], "Regression": [[40, "regression"]], "MCMC": [[40, "mcmc"]], "Variational inference": [[40, "variational-inference"]], "Interdomain inference and multioutput GPs": [[40, "interdomain-inference-and-multioutput-gps"]], "GPLVM": [[40, "gplvm"]], "Heteroskedastic models": [[40, "heteroskedastic-models"]], "Contact": [[40, "contact"]], "Citing GPflow": [[40, "citing-gpflow"]], "Acknowledgements": [[40, "acknowledgements"]], "Installation": [[41, "installation"]], "Pre-built installation": [[41, "pre-built-installation"]], "Installation from source": [[41, "installation-from-source"]], "Versions": [[41, "versions"]], "Bayesian Gaussian process latent variable model (Bayesian GPLVM)": [[42, "Bayesian-Gaussian-process-latent-variable-model-(Bayesian-GPLVM)"]], "Data": [[42, "Data"]], "Model construction": [[42, "Model-construction"]], "Model analysis": [[42, "Model-analysis"]], "Plotting vs.\u00a0Principle Component Analysis (PCA)": [[42, "Plotting-vs.\u00a0Principle-Component-Analysis-(PCA)"]], "References": [[42, "References"], [45, "References"], [64, "References"], [67, "References"], [69, "References"]], "Change points": [[43, "Change-points"]], "Convolutional Gaussian Processes": [[44, "Convolutional-Gaussian-Processes"]], "Generate dataset": [[44, "Generate-dataset"]], "Squared Exponential kernel": [[44, "Squared-Exponential-kernel"]], "Convolutional kernel": [[44, "Convolutional-kernel"]], "Conclusion": [[44, "Conclusion"]], "A simple demonstration of coregionalization": [[45, "A-simple-demonstration-of-coregionalization"]], "Data preparation": [[45, "Data-preparation"]], "Data formatting for the coregionalized model": [[45, "Data-formatting-for-the-coregionalized-model"]], "Building the coregionalization kernel": [[45, "Building-the-coregionalization-kernel"]], "Constructing the model": [[45, "Constructing-the-model"]], "Faster predictions by caching": [[46, "Faster-predictions-by-caching"]], "Posterior predictive distribution": [[46, "Posterior-predictive-distribution"]], "What can be cached?": [[46, "What-can-be-cached?"]], "GPR Example": [[46, "GPR-Example"]], "SVGP Example": [[46, "SVGP-Example"]], "SGPR Example": [[46, "SGPR-Example"]], "Stochastic Variational Inference for scalability with SVGP": [[47, "Stochastic-Variational-Inference-for-scalability-with-SVGP"]], "Generating data": [[47, "Generating-data"]], "Building the model": [[47, "Building-the-model"]], "Likelihood computation: batch vs.\u00a0minibatch": [[47, "Likelihood-computation:-batch-vs.\u00a0minibatch"]], "Stochastical estimation of ELBO": [[47, "Stochastical-estimation-of-ELBO"]], "Minibatches speed up computation": [[47, "Minibatches-speed-up-computation"]], "Running stochastic optimization": [[47, "Running-stochastic-optimization"]], "Further reading": [[47, "Further-reading"], [48, "Further-reading"], [55, "Further-reading"]], "References:": [[47, "References:"]], "Heteroskedastic Likelihood and Multi-Latent GP": [[48, "Heteroskedastic-Likelihood-and-Multi-Latent-GP"]], "Standard (Homoskedastic) Regression": [[48, "Standard-(Homoskedastic)-Regression"]], "Heteroskedastic Regression": [[48, "Heteroskedastic-Regression"]], "Data Generation": [[48, "Data-Generation"]], "Plot Data": [[48, "Plot-Data"]], "Build Model": [[48, "Build-Model"]], "Likelihood": [[48, "Likelihood"]], "Kernel": [[48, "Kernel"]], "Inducing Points": [[48, "Inducing-Points"]], "SVGP Model": [[48, "SVGP-Model"]], "Model Optimization": [[48, "Model-Optimization"]], "Build Optimizers (NatGrad + Adam)": [[48, "Build-Optimizers-(NatGrad-+-Adam)"]], "Run Optimization Loop": [[48, "Run-Optimization-Loop"]], "MCMC (Markov Chain Monte Carlo)": [[49, "MCMC-(Markov-Chain-Monte-Carlo)"]], "Example 1: GP regression": [[49, "Example-1:-GP-regression"]], "Data for a one-dimensional regression problem": [[49, "Data-for-a-one-dimensional-regression-problem"]], "MCMC for hyperparameters \\theta": [[49, "MCMC-for-hyperparameters-\\theta"]], "Example 2: Sparse MC for multiclass classification": [[49, "Example-2:-Sparse-MC-for-multiclass-classification"]], "Example 3: Fully Bayesian inference for generalized GP models with HMC": [[49, "Example-3:-Fully-Bayesian-inference-for-generalized-GP-models-with-HMC"]], "Exponential Regression": [[49, "Exponential-Regression"]], "Prior on constrained and unconstrained parameters": [[49, "Prior-on-constrained-and-unconstrained-parameters"]], "Multiclass classification": [[50, "Multiclass-classification"]], "Sampling from the GP multiclass generative model": [[50, "Sampling-from-the-GP-multiclass-generative-model"]], "Declaring model parameters and input": [[50, "Declaring-model-parameters-and-input"]], "Sampling": [[50, "Sampling"]], "Plotting": [[50, "Plotting"]], "Inference": [[50, "Inference"]], "Approximate inference: Sparse Variational Gaussian Process": [[50, "Approximate-inference:-Sparse-Variational-Gaussian-Process"]], "Declaring the SVGP model (see GPs for big data)": [[50, "Declaring-the-SVGP-model-(see-GPs-for-big-data)"]], "Running inference": [[50, "Running-inference"]], "Multi-output Gaussian processes in GPflow": [[51, "Multi-output-Gaussian-processes-in-GPflow"]], "Task": [[51, "Task"]], "Generate synthetic data": [[51, "Generate-synthetic-data"]], "Model the outputs of f(x) directly": [[51, "Model-the-outputs-of-f(x)-directly"]], "1. Shared independent multi-output kernel (MOK) and shared independent inducing variables": [[51, "1.-Shared-independent-multi-output-kernel-(MOK)-and-shared-independent-inducing-variables"]], "2. Separate independent MOK and shared independent inducing variables": [[51, "2.-Separate-independent-MOK-and-shared-independent-inducing-variables"]], "3. Separate independent kernel and separate independent inducing variables": [[51, "3.-Separate-independent-kernel-and-separate-independent-inducing-variables"]], "Model f(x) by doing inference in the g space": [[51, "Model-f(x)-by-doing-inference-in-the-g-space"]], "Mixed kernel and uncorrelated inducing variables": [[51, "Mixed-kernel-and-uncorrelated-inducing-variables"]], "Illustration of GPflow\u2019s multi-output capabilities": [[51, "Illustration-of-GPflow\u2019s-multi-output-capabilities"]], "Multi-output kernels (MOK) class diagram": [[51, "Multi-output-kernels-(MOK)-class-diagram"]], "Multi-output inducing variables class diagram": [[51, "Multi-output-inducing-variables-class-diagram"]], "Inducing points": [[51, "Inducing-points"]], "Fallback shared/separate independent inducing variables": [[51, "Fallback-shared/separate-independent-inducing-variables"]], "Shared/separate independent inducing variables": [[51, "Shared/separate-independent-inducing-variables"]], "Implemented combinations": [[51, "Implemented-combinations"]], "Debugging: introspect": [[51, "Debugging:-introspect"]], "Further Reading:": [[51, "Further-Reading:"]], "Natural gradients": [[52, "Natural-gradients"]], "VGP is a GPR": [[52, "VGP-is-a-GPR"]], "Optimize both variational parameters and kernel hyperparameters together": [[52, "Optimize-both-variational-parameters-and-kernel-hyperparameters-together"]], "Natural gradients also work for the sparse model": [[52, "Natural-gradients-also-work-for-the-sparse-model"]], "Minibatches": [[52, "Minibatches"]], "Comparison with ordinary gradients in the conjugate case": [[52, "Comparison-with-ordinary-gradients-in-the-conjugate-case"]], "Comparison with ordinary gradients in the non-conjugate case": [[52, "Comparison-with-ordinary-gradients-in-the-non-conjugate-case"]], "Binary classification": [[52, "Binary-classification"]], "Ordinal regression": [[53, "Ordinal-regression"]], "Variational Fourier Features in the GPflow framework": [[54, "Variational-Fourier-Features-in-the-GPflow-framework"]], "Gaussian process regression with varying output noise": [[55, "Gaussian-process-regression-with-varying-output-noise"]], "Demo 1: known noise variances": [[55, "Demo-1:-known-noise-variances"]], "Generate data": [[55, "Generate-data"], [55, "id1"], [55, "id2"]], "Try a naive fit": [[55, "Try-a-naive-fit"]], "Fit a polynomial to the noise scale": [[55, "Fit-a-polynomial-to-the-noise-scale"]], "Demo 2: grouped noise variances": [[55, "Demo-2:-grouped-noise-variances"]], "Fit a naive model": [[55, "Fit-a-naive-model"], [55, "id4"]], "Data structure": [[55, "Data-structure"], [55, "id3"]], "Use multiple functions for the noise variance": [[55, "Use-multiple-functions-for-the-noise-variance"]], "Demo 3: Empirical noise variance": [[55, "Demo-3:-Empirical-noise-variance"]], "Create custom function for the noise variance": [[55, "Create-custom-function-for-the-noise-variance"]], "Basic Usage with GPR": [[56, "Basic-Usage-with-GPR"]], "Imports": [[56, "Imports"]], "Meet f and Y": [[56, "Meet-f-and-Y"]], "Minimal model": [[56, "Minimal-model"]], "Plotting the model": [[56, "Plotting-the-model"]], "Marginal variance vs full covariance": [[56, "Marginal-variance-vs-full-covariance"]], "What\u2019s next?": [[56, "What\u2019s-next?"]], "Classification, other data distributions, VGP and SVGP": [[57, "Classification,-other-data-distributions,-VGP-and-SVGP"]], "The Variational Gaussion Process": [[57, "The-Variational-Gaussion-Process"]], "Non-gaussian regression": [[57, "Non-gaussian-regression"]], "Classification": [[57, "Classification"]], "The Sparse Variational Gaussian Process": [[57, "The-Sparse-Variational-Gaussian-Process"]], "Writing code that handles both internal and external data models": [[57, "Writing-code-that-handles-both-internal-and-external-data-models"]], "Kernels": [[58, "Kernels"]], "What is a kernel?": [[58, "What-is-a-kernel?"]], "Visualising a kernel": [[58, "Visualising-a-kernel"]], "The Mat\u00e9rn family": [[58, "The-Mat\u00e9rn-family"]], "Kernel parameters": [[58, "Kernel-parameters"]], "Kernel composition": [[58, "Kernel-composition"]], "Periodic": [[58, "Periodic"]], "Change-points": [[58, "Change-points"]], "Some other simple kernels": [[58, "Some-other-simple-kernels"]], "Addition and multiplication": [[58, "Addition-and-multiplication"]], "Multiple-dimensional data": [[58, "Multiple-dimensional-data"]], "Multi-dimensional parameters": [[58, "Multi-dimensional-parameters"]], "Active dimensions": [[58, "Active-dimensions"]], "Large Data with SGPR": [[59, "Large-Data-with-SGPR"]], "Picking initial inducing points": [[59, "Picking-initial-inducing-points"]], "Random data samples": [[59, "Random-data-samples"]], "k-means": [[59, "k-means"]], "Uncorrelated samples": [[59, "Uncorrelated-samples"]], "Advanced initialisation": [[59, "Advanced-initialisation"]], "Mean Functions": [[60, "Mean-Functions"]], "Mean reversion": [[60, "Mean-reversion"]], "Setting a mean function": [[60, "Setting-a-mean-function"]], "Interactions with the kernel": [[60, "Interactions-with-the-kernel"]], "Kernels versus mean functions": [[60, "Kernels-versus-mean-functions"]], "Custom mean functions": [[60, "Custom-mean-functions"]], "Composition": [[60, "Composition"]], "Monitoring": [[61, "Monitoring"]], "Components of monitoring": [[61, "Components-of-monitoring"]], "ExecuteCallback": [[61, "ExecuteCallback"]], "TensorBoard integration": [[61, "TensorBoard-integration"]], "Parameters and Their Optimisation": [[62, "Parameters-and-Their-Optimisation"]], "The Module and Parameter classes": [[62, "The-Module-and-Parameter-classes"]], "Inspecting parameters": [[62, "Inspecting-parameters"]], "Setting parameters": [[62, "Setting-parameters"]], "Optimisation": [[62, "Optimisation"]], "What to do if you model fails to fit": [[62, "What-to-do-if-you-model-fails-to-fit"]], "Dataset: CO_2 levels": [[62, "Dataset:-CO_2-levels"]], "Setting the initial value": [[62, "Setting-the-initial-value"]], "Priors": [[62, "Priors"]], "Transforms": [[62, "Transforms"]], "Trainable parameters": [[62, "Trainable-parameters"]], "Advanced training": [[62, "Advanced-training"]], "Multi-stage training": [[62, "Multi-stage-training"]], "The Keras optimisers": [[62, "The-Keras-optimisers"]], "Saving and Loading Models": [[63, "Saving-and-Loading-Models"]], "Checkpointing": [[63, "Checkpointing"]], "TensorFlow saved_model": [[63, "TensorFlow-saved_model"]], "Copying (hyper)parameter values between models": [[63, "Copying-(hyper)parameter-values-between-models"]], "Which method to use": [[63, "Which-method-to-use"]], "Custom mean functions: metalearning with GPs": [[64, "Custom-mean-functions:-metalearning-with-GPs"]], "Generate the tasks": [[64, "Generate-the-tasks"]], "Create the mean function": [[64, "Create-the-mean-function"]], "Build the GP metamodel": [[64, "Build-the-GP-metamodel"]], "Assess the model": [[64, "Assess-the-model"]], "Mixing TensorFlow models with GPflow": [[65, "Mixing-TensorFlow-models-with-GPflow"]], "Convolutional network inside a GPflow model": [[65, "Convolutional-network-inside-a-GPflow-model"]], "Kernel Design": [[66, "Kernel-Design"]], "__init__": [[66, "__init__"]], "K": [[66, "K"]], "K_diag": [[66, "K_diag"]], "Using the kernel in a model": [[66, "Using-the-kernel-in-a-model"]], "See also": [[66, "See-also"]], "Mixture Density Networks in GPflow": [[67, "Mixture-Density-Networks-in-GPflow"]], "Conditional Density Estimation models": [[67, "Conditional-Density-Estimation-models"]], "Mixture Density Network models": [[67, "Mixture-Density-Network-models"]], "A GPflow MDN implementation": [[67, "A-GPflow-MDN-implementation"]], "Notes": [[67, "Notes"]], "Experiment 1: The sinusoidal dataset": [[67, "Experiment-1:-The-sinusoidal-dataset"]], "Experiment 2: The half moon dataset": [[67, "Experiment-2:-The-half-moon-dataset"]], "Comparing FITC approximation to VFE approximation": [[68, "Comparing-FITC-approximation-to-VFE-approximation"]], "Derivation of SGPR equations": [[69, "Derivation-of-SGPR-equations"]], "Marginal likelihood bound": [[69, "Marginal-likelihood-bound"]], "Prediction": [[69, "Prediction"], [73, "Prediction"]], "Sanity checking when model behaviours should overlap": [[70, "Sanity-checking-when-model-behaviours-should-overlap"]], "Conjugate Gradient Lower Bound": [[71, "Conjugate-Gradient-Lower-Bound"]], "Discussion of the GP marginal likelihood upper bound": [[72, "Discussion-of-the-GP-marginal-likelihood-upper-bound"]], "Full model": [[72, "Full-model"]], "Upper bounds for sparse variational models": [[72, "Upper-bounds-for-sparse-variational-models"]], "Upper bounds for fixed hyperparameters": [[72, "Upper-bounds-for-fixed-hyperparameters"]], "A tight estimate bound does not imply a converged model": [[72, "A-tight-estimate-bound-does-not-imply-a-converged-model"]], "Derivation of VGP equations": [[73, "Derivation-of-VGP-equations"]], "Optimal distribution": [[73, "Optimal-distribution"]], "Marginals of q(\\mathbf f)": [[73, "Marginals-of-q(\\mathbf-f)"]], "KL divergence": [[73, "KL-divergence"]], "User Guide": [[74, "user-guide"]], "Theoretical notes": [[74, "theoretical-notes"]], "Tailored models": [[74, "tailored-models"]], "Advanced needs": [[74, "advanced-needs"]]}, "indexentries": {"prioron (class in gpflow.base)": [[0, "gpflow.base.PriorOn"]], "gpflow.base": [[0, "module-gpflow.base"]], "module": [[0, "module-gpflow.base"], [1, "module-gpflow.conditionals"], [2, "module-gpflow.conditionals.util"], [3, "module-gpflow.config"], [4, "module-gpflow.covariances"], [5, "module-gpflow.expectations"], [6, "module-gpflow.expectations.quadratures"], [7, "module-gpflow.experimental"], [8, "module-gpflow.experimental.utils"], [9, "module-gpflow.functions"], [10, "module-gpflow"], [11, "module-gpflow.inducing_variables"], [12, "module-gpflow.inducing_variables.inducing_variables"], [13, "module-gpflow.kernels.base"], [14, "module-gpflow.kernels"], [15, "module-gpflow.kullback_leiblers"], [16, "module-gpflow.likelihoods"], [17, "module-gpflow.likelihoods.utils"], [18, "module-gpflow.logdensities"], [19, "module-gpflow.models.cglb"], [20, "module-gpflow.models.gpr"], [21, "module-gpflow.models"], [22, "module-gpflow.models.sgpr"], [23, "module-gpflow.models.svgp"], [24, "module-gpflow.models.util"], [25, "module-gpflow.models.vgp"], [26, "module-gpflow.monitor"], [27, "module-gpflow.optimizers"], [28, "module-gpflow.optimizers.natgrad"], [29, "module-gpflow.posteriors"], [30, "module-gpflow.probability_distributions"], [31, "module-gpflow.quadrature.gauss_hermite"], [32, "module-gpflow.quadrature"], [33, "module-gpflow.type_flags"], [34, "module-gpflow.utilities"], [35, "module-gpflow.utilities.ops"], [36, "module-gpflow.utilities.parameter_or_function"]], "_dense_conditional() (in module gpflow.conditionals.conditionals)": [[1, "gpflow.conditionals.conditionals._dense_conditional"]], "_sample_conditional() (in module gpflow.conditionals.multioutput.sample_conditionals)": [[1, "gpflow.conditionals.multioutput.sample_conditionals._sample_conditional"]], "_sample_conditional() (in module gpflow.conditionals.sample_conditionals)": [[1, "gpflow.conditionals.sample_conditionals._sample_conditional"]], "_sparse_conditional() (in module gpflow.conditionals.conditionals)": [[1, "gpflow.conditionals.conditionals._sparse_conditional"]], "base_conditional() (in module gpflow.conditionals)": [[1, "gpflow.conditionals.base_conditional"]], "coregionalization_conditional() (in module gpflow.conditionals.multioutput.conditionals)": [[1, "gpflow.conditionals.multioutput.conditionals.coregionalization_conditional"]], "fallback_independent_latent_conditional() (in module gpflow.conditionals.multioutput.conditionals)": [[1, "gpflow.conditionals.multioutput.conditionals.fallback_independent_latent_conditional"]], "gpflow.conditionals": [[1, "module-gpflow.conditionals"]], "inducing_point_conditional() (in module gpflow.conditionals.multioutput.conditionals)": [[1, "gpflow.conditionals.multioutput.conditionals.inducing_point_conditional"]], "separate_independent_conditional() (in module gpflow.conditionals.multioutput.conditionals)": [[1, "gpflow.conditionals.multioutput.conditionals.separate_independent_conditional"]], "shared_independent_conditional() (in module gpflow.conditionals.multioutput.conditionals)": [[1, "gpflow.conditionals.multioutput.conditionals.shared_independent_conditional"]], "uncertain_conditional() (in module gpflow.conditionals)": [[1, "gpflow.conditionals.uncertain_conditional"]], "base_conditional_with_lm() (in module gpflow.conditionals.util)": [[2, "gpflow.conditionals.util.base_conditional_with_lm"]], "expand_independent_outputs() (in module gpflow.conditionals.util)": [[2, "gpflow.conditionals.util.expand_independent_outputs"]], "fully_correlated_conditional() (in module gpflow.conditionals.util)": [[2, "gpflow.conditionals.util.fully_correlated_conditional"]], "fully_correlated_conditional_repeat() (in module gpflow.conditionals.util)": [[2, "gpflow.conditionals.util.fully_correlated_conditional_repeat"]], "gpflow.conditionals.util": [[2, "module-gpflow.conditionals.util"]], "independent_interdomain_conditional() (in module gpflow.conditionals.util)": [[2, "gpflow.conditionals.util.independent_interdomain_conditional"]], "mix_latent_gp() (in module gpflow.conditionals.util)": [[2, "gpflow.conditionals.util.mix_latent_gp"]], "rollaxis_left() (in module gpflow.conditionals.util)": [[2, "gpflow.conditionals.util.rollaxis_left"]], "rollaxis_right() (in module gpflow.conditionals.util)": [[2, "gpflow.conditionals.util.rollaxis_right"]], "sample_mvn() (in module gpflow.conditionals.util)": [[2, "gpflow.conditionals.util.sample_mvn"]], "separate_independent_conditional_implementation() (in module gpflow.conditionals.util)": [[2, "gpflow.conditionals.util.separate_independent_conditional_implementation"]], "config (class in gpflow.config)": [[3, "gpflow.config.Config"]], "as_context() (in module gpflow.config)": [[3, "gpflow.config.as_context"]], "config() (in module gpflow.config)": [[3, "gpflow.config.config"]], "default_positive_bijector() (in module gpflow.config)": [[3, "gpflow.config.default_positive_bijector"]], "default_positive_minimum() (in module gpflow.config)": [[3, "gpflow.config.default_positive_minimum"]], "default_summary_fmt() (in module gpflow.config)": [[3, "gpflow.config.default_summary_fmt"]], "float (gpflow.config.config attribute)": [[3, "gpflow.config.Config.float"]], "gpflow.config": [[3, "module-gpflow.config"]], "int (gpflow.config.config attribute)": [[3, "gpflow.config.Config.int"]], "jitter (gpflow.config.config attribute)": [[3, "gpflow.config.Config.jitter"]], "positive_bijector (gpflow.config.config attribute)": [[3, "gpflow.config.Config.positive_bijector"]], "positive_bijector_type_map() (in module gpflow.config)": [[3, "gpflow.config.positive_bijector_type_map"]], "positive_minimum (gpflow.config.config attribute)": [[3, "gpflow.config.Config.positive_minimum"]], "set_config() (in module gpflow.config)": [[3, "gpflow.config.set_config"]], "set_default_float() (in module gpflow.config)": [[3, "gpflow.config.set_default_float"]], "set_default_int() (in module gpflow.config)": [[3, "gpflow.config.set_default_int"]], "set_default_jitter() (in module gpflow.config)": [[3, "gpflow.config.set_default_jitter"]], "set_default_positive_bijector() (in module gpflow.config)": [[3, "gpflow.config.set_default_positive_bijector"]], "set_default_positive_minimum() (in module gpflow.config)": [[3, "gpflow.config.set_default_positive_minimum"]], "set_default_summary_fmt() (in module gpflow.config)": [[3, "gpflow.config.set_default_summary_fmt"]], "summary_fmt (gpflow.config.config attribute)": [[3, "gpflow.config.Config.summary_fmt"]], "kuf_conv_patch() (in module gpflow.covariances.kufs)": [[4, "gpflow.covariances.kufs.Kuf_conv_patch"]], "kuf_fallback_separate_linear_coregionalization() (in module gpflow.covariances.multioutput.kufs)": [[4, "gpflow.covariances.multioutput.kufs.Kuf_fallback_separate_linear_coregionalization"]], "kuf_fallback_shared_linear_coregionalization() (in module gpflow.covariances.multioutput.kufs)": [[4, "gpflow.covariances.multioutput.kufs.Kuf_fallback_shared_linear_coregionalization"]], "kuf_generic() (in module gpflow.covariances.multioutput.kufs)": [[4, "gpflow.covariances.multioutput.kufs.Kuf_generic"]], "kuf_kernel_inducingpoints() (in module gpflow.covariances.kufs)": [[4, "gpflow.covariances.kufs.Kuf_kernel_inducingpoints"]], "kuf_separate_linear_coregionalization() (in module gpflow.covariances.multioutput.kufs)": [[4, "gpflow.covariances.multioutput.kufs.Kuf_separate_linear_coregionalization"]], "kuf_separate_separate() (in module gpflow.covariances.multioutput.kufs)": [[4, "gpflow.covariances.multioutput.kufs.Kuf_separate_separate"]], "kuf_separate_shared() (in module gpflow.covariances.multioutput.kufs)": [[4, "gpflow.covariances.multioutput.kufs.Kuf_separate_shared"]], "kuf_shared_linear_coregionalization() (in module gpflow.covariances.multioutput.kufs)": [[4, "gpflow.covariances.multioutput.kufs.Kuf_shared_linear_coregionalization"]], "kuf_shared_separate() (in module gpflow.covariances.multioutput.kufs)": [[4, "gpflow.covariances.multioutput.kufs.Kuf_shared_separate"]], "kuf_shared_shared() (in module gpflow.covariances.multioutput.kufs)": [[4, "gpflow.covariances.multioutput.kufs.Kuf_shared_shared"]], "kuf_sqexp_multiscale() (in module gpflow.covariances.kufs)": [[4, "gpflow.covariances.kufs.Kuf_sqexp_multiscale"]], "kuu_conv_patch() (in module gpflow.covariances.kuus)": [[4, "gpflow.covariances.kuus.Kuu_conv_patch"]], "kuu_fallbace_separate() (in module gpflow.covariances.multioutput.kuus)": [[4, "gpflow.covariances.multioutput.kuus.Kuu_fallbace_separate"]], "kuu_fallback_separate_shared() (in module gpflow.covariances.multioutput.kuus)": [[4, "gpflow.covariances.multioutput.kuus.Kuu_fallback_separate_shared"]], "kuu_fallback_shared() (in module gpflow.covariances.multioutput.kuus)": [[4, "gpflow.covariances.multioutput.kuus.Kuu_fallback_shared"]], "kuu_generic() (in module gpflow.covariances.multioutput.kuus)": [[4, "gpflow.covariances.multioutput.kuus.Kuu_generic"]], "kuu_kernel_inducingpoints() (in module gpflow.covariances.kuus)": [[4, "gpflow.covariances.kuus.Kuu_kernel_inducingpoints"]], "kuu_shared_shared() (in module gpflow.covariances.multioutput.kuus)": [[4, "gpflow.covariances.multioutput.kuus.Kuu_shared_shared"]], "kuu_sqexp_multiscale() (in module gpflow.covariances.kuus)": [[4, "gpflow.covariances.kuus.Kuu_sqexp_multiscale"]], "gpflow.covariances": [[4, "module-gpflow.covariances"]], "expectation() (in module gpflow.expectations)": [[5, "gpflow.expectations.expectation"]], "gpflow.expectations": [[5, "module-gpflow.expectations"]], "quadrature_expectation() (in module gpflow.expectations)": [[5, "gpflow.expectations.quadrature_expectation"]], "get_eval_func() (in module gpflow.expectations.quadratures)": [[6, "gpflow.expectations.quadratures.get_eval_func"]], "gpflow.expectations.quadratures": [[6, "module-gpflow.expectations.quadratures"]], "gpflow.experimental": [[7, "module-gpflow.experimental"]], "experimental() (in module gpflow.experimental.utils)": [[8, "gpflow.experimental.utils.experimental"]], "gpflow.experimental.utils": [[8, "module-gpflow.experimental.utils"]], "additive (class in gpflow.functions)": [[9, "gpflow.functions.Additive"]], "constant (class in gpflow.functions)": [[9, "gpflow.functions.Constant"]], "function (class in gpflow.functions)": [[9, "gpflow.functions.Function"]], "identity (class in gpflow.functions)": [[9, "gpflow.functions.Identity"]], "linear (class in gpflow.functions)": [[9, "gpflow.functions.Linear"]], "meanfunction (class in gpflow.functions)": [[9, "gpflow.functions.MeanFunction"]], "polynomial (class in gpflow.functions)": [[9, "gpflow.functions.Polynomial"]], "product (class in gpflow.functions)": [[9, "gpflow.functions.Product"]], "switchedfunction (class in gpflow.functions)": [[9, "gpflow.functions.SwitchedFunction"]], "switchedmeanfunction (class in gpflow.functions)": [[9, "gpflow.functions.SwitchedMeanFunction"]], "zero (class in gpflow.functions)": [[9, "gpflow.functions.Zero"]], "compute_powers() (gpflow.functions.polynomial static method)": [[9, "gpflow.functions.Polynomial.compute_powers"]], "gpflow.functions": [[9, "module-gpflow.functions"]], "module (class in gpflow)": [[10, "gpflow.Module"]], "parameter (class in gpflow)": [[10, "gpflow.Parameter"]], "assign() (gpflow.parameter method)": [[10, "gpflow.Parameter.assign"]], "default_float() (in module gpflow)": [[10, "gpflow.default_float"]], "default_int() (in module gpflow)": [[10, "gpflow.default_int"]], "default_jitter() (in module gpflow)": [[10, "gpflow.default_jitter"]], "gpflow": [[10, "module-gpflow"]], "log_prior_density() (gpflow.parameter method)": [[10, "gpflow.Parameter.log_prior_density"]], "set_trainable() (in module gpflow)": [[10, "gpflow.set_trainable"]], "trainable (gpflow.parameter property)": [[10, "gpflow.Parameter.trainable"]], "fallbackseparateindependentinducingvariables (class in gpflow.inducing_variables)": [[11, "gpflow.inducing_variables.FallbackSeparateIndependentInducingVariables"]], "fallbacksharedindependentinducingvariables (class in gpflow.inducing_variables)": [[11, "gpflow.inducing_variables.FallbackSharedIndependentInducingVariables"]], "inducingpatches (class in gpflow.inducing_variables)": [[11, "gpflow.inducing_variables.InducingPatches"]], "inducingpoints (class in gpflow.inducing_variables)": [[11, "gpflow.inducing_variables.InducingPoints"]], "inducingvariables (class in gpflow.inducing_variables)": [[11, "gpflow.inducing_variables.InducingVariables"]], "multioutputinducingvariables (class in gpflow.inducing_variables)": [[11, "gpflow.inducing_variables.MultioutputInducingVariables"]], "multiscale (class in gpflow.inducing_variables)": [[11, "gpflow.inducing_variables.Multiscale"]], "separateindependentinducingvariables (class in gpflow.inducing_variables)": [[11, "gpflow.inducing_variables.SeparateIndependentInducingVariables"]], "sharedindependentinducingvariables (class in gpflow.inducing_variables)": [[11, "gpflow.inducing_variables.SharedIndependentInducingVariables"]], "gpflow.inducing_variables": [[11, "module-gpflow.inducing_variables"]], "num_inducing (gpflow.inducing_variables.fallbackseparateindependentinducingvariables property)": [[11, "gpflow.inducing_variables.FallbackSeparateIndependentInducingVariables.num_inducing"]], "num_inducing (gpflow.inducing_variables.fallbacksharedindependentinducingvariables property)": [[11, "gpflow.inducing_variables.FallbackSharedIndependentInducingVariables.num_inducing"]], "num_inducing (gpflow.inducing_variables.inducingvariables property)": [[11, "gpflow.inducing_variables.InducingVariables.num_inducing"]], "shape (gpflow.inducing_variables.fallbackseparateindependentinducingvariables property)": [[11, "gpflow.inducing_variables.FallbackSeparateIndependentInducingVariables.shape"]], "shape (gpflow.inducing_variables.fallbacksharedindependentinducingvariables property)": [[11, "gpflow.inducing_variables.FallbackSharedIndependentInducingVariables.shape"]], "shape (gpflow.inducing_variables.inducingvariables property)": [[11, "gpflow.inducing_variables.InducingVariables.shape"]], "inducingpointsbase (class in gpflow.inducing_variables.inducing_variables)": [[12, "gpflow.inducing_variables.inducing_variables.InducingPointsBase"]], "gpflow.inducing_variables.inducing_variables": [[12, "module-gpflow.inducing_variables.inducing_variables"]], "num_inducing (gpflow.inducing_variables.inducing_variables.inducingpointsbase property)": [[12, "gpflow.inducing_variables.inducing_variables.InducingPointsBase.num_inducing"]], "shape (gpflow.inducing_variables.inducing_variables.inducingpointsbase property)": [[12, "gpflow.inducing_variables.inducing_variables.InducingPointsBase.shape"]], "reducingcombination (class in gpflow.kernels.base)": [[13, "gpflow.kernels.base.ReducingCombination"]], "gpflow.kernels.base": [[13, "module-gpflow.kernels.base"]], "anisotropicstationary (class in gpflow.kernels)": [[14, "gpflow.kernels.AnisotropicStationary"]], "arccosine (class in gpflow.kernels)": [[14, "gpflow.kernels.ArcCosine"]], "bias (in module gpflow.kernels)": [[14, "gpflow.kernels.Bias"]], "changepoints (class in gpflow.kernels)": [[14, "gpflow.kernels.ChangePoints"]], "combination (class in gpflow.kernels)": [[14, "gpflow.kernels.Combination"]], "convolutional (class in gpflow.kernels)": [[14, "gpflow.kernels.Convolutional"]], "coregion (class in gpflow.kernels)": [[14, "gpflow.kernels.Coregion"]], "cosine (class in gpflow.kernels)": [[14, "gpflow.kernels.Cosine"]], "exponential (class in gpflow.kernels)": [[14, "gpflow.kernels.Exponential"]], "independentlatent (class in gpflow.kernels)": [[14, "gpflow.kernels.IndependentLatent"]], "isotropicstationary (class in gpflow.kernels)": [[14, "gpflow.kernels.IsotropicStationary"]], "k() (gpflow.kernels.linearcoregionalization method)": [[14, "gpflow.kernels.LinearCoregionalization.K"]], "k() (gpflow.kernels.multioutputkernel method)": [[14, "gpflow.kernels.MultioutputKernel.K"]], "k() (gpflow.kernels.separateindependent method)": [[14, "gpflow.kernels.SeparateIndependent.K"]], "k() (gpflow.kernels.sharedindependent method)": [[14, "gpflow.kernels.SharedIndependent.K"]], "k_diag() (gpflow.kernels.linearcoregionalization method)": [[14, "gpflow.kernels.LinearCoregionalization.K_diag"]], "k_diag() (gpflow.kernels.multioutputkernel method)": [[14, "gpflow.kernels.MultioutputKernel.K_diag"]], "k_diag() (gpflow.kernels.separateindependent method)": [[14, "gpflow.kernels.SeparateIndependent.K_diag"]], "k_diag() (gpflow.kernels.sharedindependent method)": [[14, "gpflow.kernels.SharedIndependent.K_diag"]], "kernel (class in gpflow.kernels)": [[14, "gpflow.kernels.Kernel"]], "linear (class in gpflow.kernels)": [[14, "gpflow.kernels.Linear"]], "linearcoregionalization (class in gpflow.kernels)": [[14, "gpflow.kernels.LinearCoregionalization"]], "matern12 (class in gpflow.kernels)": [[14, "gpflow.kernels.Matern12"]], "matern32 (class in gpflow.kernels)": [[14, "gpflow.kernels.Matern32"]], "matern52 (class in gpflow.kernels)": [[14, "gpflow.kernels.Matern52"]], "multioutputkernel (class in gpflow.kernels)": [[14, "gpflow.kernels.MultioutputKernel"]], "periodic (class in gpflow.kernels)": [[14, "gpflow.kernels.Periodic"]], "polynomial (class in gpflow.kernels)": [[14, "gpflow.kernels.Polynomial"]], "product (class in gpflow.kernels)": [[14, "gpflow.kernels.Product"]], "rbf (in module gpflow.kernels)": [[14, "gpflow.kernels.RBF"]], "rationalquadratic (class in gpflow.kernels)": [[14, "gpflow.kernels.RationalQuadratic"]], "separateindependent (class in gpflow.kernels)": [[14, "gpflow.kernels.SeparateIndependent"]], "sharedindependent (class in gpflow.kernels)": [[14, "gpflow.kernels.SharedIndependent"]], "static (class in gpflow.kernels)": [[14, "gpflow.kernels.Static"]], "stationary (class in gpflow.kernels)": [[14, "gpflow.kernels.Stationary"]], "sum (class in gpflow.kernels)": [[14, "gpflow.kernels.Sum"]], "white (class in gpflow.kernels)": [[14, "gpflow.kernels.White"]], "ard (gpflow.kernels.arccosine property)": [[14, "gpflow.kernels.ArcCosine.ard"]], "ard (gpflow.kernels.linear property)": [[14, "gpflow.kernels.Linear.ard"]], "ard (gpflow.kernels.stationary property)": [[14, "gpflow.kernels.Stationary.ard"]], "get_patches() (gpflow.kernels.convolutional method)": [[14, "gpflow.kernels.Convolutional.get_patches"]], "gpflow.kernels": [[14, "module-gpflow.kernels"]], "latent_kernels (gpflow.kernels.linearcoregionalization property)": [[14, "gpflow.kernels.LinearCoregionalization.latent_kernels"]], "latent_kernels (gpflow.kernels.multioutputkernel property)": [[14, "gpflow.kernels.MultioutputKernel.latent_kernels"]], "latent_kernels (gpflow.kernels.separateindependent property)": [[14, "gpflow.kernels.SeparateIndependent.latent_kernels"]], "latent_kernels (gpflow.kernels.sharedindependent property)": [[14, "gpflow.kernels.SharedIndependent.latent_kernels"]], "num_latent_gps (gpflow.kernels.linearcoregionalization property)": [[14, "gpflow.kernels.LinearCoregionalization.num_latent_gps"]], "num_latent_gps (gpflow.kernels.multioutputkernel property)": [[14, "gpflow.kernels.MultioutputKernel.num_latent_gps"]], "num_latent_gps (gpflow.kernels.separateindependent property)": [[14, "gpflow.kernels.SeparateIndependent.num_latent_gps"]], "num_latent_gps (gpflow.kernels.sharedindependent property)": [[14, "gpflow.kernels.SharedIndependent.num_latent_gps"]], "on_separate_dimensions (gpflow.kernels.combination property)": [[14, "gpflow.kernels.Combination.on_separate_dimensions"]], "on_separate_dims() (gpflow.kernels.kernel method)": [[14, "gpflow.kernels.Kernel.on_separate_dims"]], "scaled_difference_matrix() (gpflow.kernels.anisotropicstationary method)": [[14, "gpflow.kernels.AnisotropicStationary.scaled_difference_matrix"]], "scaled_squared_euclid_dist() (gpflow.kernels.isotropicstationary method)": [[14, "gpflow.kernels.IsotropicStationary.scaled_squared_euclid_dist"]], "slice() (gpflow.kernels.kernel method)": [[14, "gpflow.kernels.Kernel.slice"]], "slice_cov() (gpflow.kernels.kernel method)": [[14, "gpflow.kernels.Kernel.slice_cov"]], "_() (in module gpflow.kullback_leiblers)": [[15, "gpflow.kullback_leiblers._"]], "gauss_kl() (in module gpflow.kullback_leiblers)": [[15, "gpflow.kullback_leiblers.gauss_kl"]], "gpflow.kullback_leiblers": [[15, "module-gpflow.kullback_leiblers"]], "bernoulli (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.Bernoulli"]], "beta (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.Beta"]], "exponential (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.Exponential"]], "gamma (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.Gamma"]], "gaussian (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.Gaussian"]], "gaussianmc (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.GaussianMC"]], "heteroskedastictfpconditional (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.HeteroskedasticTFPConditional"]], "likelihood (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.Likelihood"]], "montecarlolikelihood (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.MonteCarloLikelihood"]], "multiclass (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.MultiClass"]], "multilatentlikelihood (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.MultiLatentLikelihood"]], "multilatenttfpconditional (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.MultiLatentTFPConditional"]], "ordinal (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.Ordinal"]], "poisson (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.Poisson"]], "quadraturelikelihood (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.QuadratureLikelihood"]], "robustmax (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.RobustMax"]], "scalarlikelihood (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.ScalarLikelihood"]], "softmax (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.Softmax"]], "studentt (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.StudentT"]], "switchedlikelihood (class in gpflow.likelihoods)": [[16, "gpflow.likelihoods.SwitchedLikelihood"]], "conditional_mean() (gpflow.likelihoods.likelihood method)": [[16, "gpflow.likelihoods.Likelihood.conditional_mean"]], "conditional_variance() (gpflow.likelihoods.likelihood method)": [[16, "gpflow.likelihoods.Likelihood.conditional_variance"]], "gpflow.likelihoods": [[16, "module-gpflow.likelihoods"]], "log_prob() (gpflow.likelihoods.likelihood method)": [[16, "gpflow.likelihoods.Likelihood.log_prob"]], "predict_log_density() (gpflow.likelihoods.likelihood method)": [[16, "gpflow.likelihoods.Likelihood.predict_log_density"]], "predict_mean_and_var() (gpflow.likelihoods.likelihood method)": [[16, "gpflow.likelihoods.Likelihood.predict_mean_and_var"]], "variational_expectations() (gpflow.likelihoods.likelihood method)": [[16, "gpflow.likelihoods.Likelihood.variational_expectations"]], "gpflow.likelihoods.utils": [[17, "module-gpflow.likelihoods.utils"]], "inv_probit() (in module gpflow.likelihoods.utils)": [[17, "gpflow.likelihoods.utils.inv_probit"]], "bernoulli() (in module gpflow.logdensities)": [[18, "gpflow.logdensities.bernoulli"]], "beta() (in module gpflow.logdensities)": [[18, "gpflow.logdensities.beta"]], "exponential() (in module gpflow.logdensities)": [[18, "gpflow.logdensities.exponential"]], "gamma() (in module gpflow.logdensities)": [[18, "gpflow.logdensities.gamma"]], "gaussian() (in module gpflow.logdensities)": [[18, "gpflow.logdensities.gaussian"]], "gpflow.logdensities": [[18, "module-gpflow.logdensities"]], "laplace() (in module gpflow.logdensities)": [[18, "gpflow.logdensities.laplace"]], "lognormal() (in module gpflow.logdensities)": [[18, "gpflow.logdensities.lognormal"]], "multivariate_normal() (in module gpflow.logdensities)": [[18, "gpflow.logdensities.multivariate_normal"]], "poisson() (in module gpflow.logdensities)": [[18, "gpflow.logdensities.poisson"]], "student_t() (in module gpflow.logdensities)": [[18, "gpflow.logdensities.student_t"]], "nystrompreconditioner (class in gpflow.models.cglb)": [[19, "gpflow.models.cglb.NystromPreconditioner"]], "cglb_conjugate_gradient() (in module gpflow.models.cglb)": [[19, "gpflow.models.cglb.cglb_conjugate_gradient"]], "gpflow.models.cglb": [[19, "module-gpflow.models.cglb"]], "gpr_deprecated (class in gpflow.models.gpr)": [[20, "gpflow.models.gpr.GPR_deprecated"]], "gpr_with_posterior (class in gpflow.models.gpr)": [[20, "gpflow.models.gpr.GPR_with_posterior"]], "gpflow.models.gpr": [[20, "module-gpflow.models.gpr"]], "log_marginal_likelihood() (gpflow.models.gpr.gpr_deprecated method)": [[20, "gpflow.models.gpr.GPR_deprecated.log_marginal_likelihood"]], "maximum_log_likelihood_objective() (gpflow.models.gpr.gpr_deprecated method)": [[20, "gpflow.models.gpr.GPR_deprecated.maximum_log_likelihood_objective"]], "posterior() (gpflow.models.gpr.gpr_with_posterior method)": [[20, "gpflow.models.gpr.GPR_with_posterior.posterior"]], "predict_f() (gpflow.models.gpr.gpr_deprecated method)": [[20, "gpflow.models.gpr.GPR_deprecated.predict_f"]], "predict_f() (gpflow.models.gpr.gpr_with_posterior method)": [[20, "gpflow.models.gpr.GPR_with_posterior.predict_f"]], "bayesiangplvm (class in gpflow.models)": [[21, "gpflow.models.BayesianGPLVM"]], "bayesianmodel (class in gpflow.models)": [[21, "gpflow.models.BayesianModel"]], "cglb (class in gpflow.models)": [[21, "gpflow.models.CGLB"]], "externaldatatraininglossmixin (class in gpflow.models)": [[21, "gpflow.models.ExternalDataTrainingLossMixin"]], "gplvm (class in gpflow.models)": [[21, "gpflow.models.GPLVM"]], "gpmc (class in gpflow.models)": [[21, "gpflow.models.GPMC"]], "gpmodel (class in gpflow.models)": [[21, "gpflow.models.GPModel"]], "gpr (class in gpflow.models)": [[21, "gpflow.models.GPR"]], "gprfitc (class in gpflow.models)": [[21, "gpflow.models.GPRFITC"]], "internaldatatraininglossmixin (class in gpflow.models)": [[21, "gpflow.models.InternalDataTrainingLossMixin"]], "sgpmc (class in gpflow.models)": [[21, "gpflow.models.SGPMC"]], "sgpr (class in gpflow.models)": [[21, "gpflow.models.SGPR"]], "svgp (class in gpflow.models)": [[21, "gpflow.models.SVGP"]], "vgp (class in gpflow.models)": [[21, "gpflow.models.VGP"]], "vgpopperarchambeau (class in gpflow.models)": [[21, "gpflow.models.VGPOpperArchambeau"]], "calc_num_latent_gps() (gpflow.models.gpmodel static method)": [[21, "gpflow.models.GPModel.calc_num_latent_gps"]], "calc_num_latent_gps_from_data() (gpflow.models.gpmodel static method)": [[21, "gpflow.models.GPModel.calc_num_latent_gps_from_data"]], "elbo() (gpflow.models.bayesiangplvm method)": [[21, "gpflow.models.BayesianGPLVM.elbo"]], "elbo() (gpflow.models.vgpopperarchambeau method)": [[21, "gpflow.models.VGPOpperArchambeau.elbo"]], "fitc_log_marginal_likelihood() (gpflow.models.gprfitc method)": [[21, "gpflow.models.GPRFITC.fitc_log_marginal_likelihood"]], "gpflow.models": [[21, "module-gpflow.models"]], "log_likelihood() (gpflow.models.gpmc method)": [[21, "gpflow.models.GPMC.log_likelihood"]], "log_likelihood_lower_bound() (gpflow.models.sgpmc method)": [[21, "gpflow.models.SGPMC.log_likelihood_lower_bound"]], "log_posterior_density() (gpflow.models.bayesianmodel method)": [[21, "gpflow.models.BayesianModel.log_posterior_density"]], "log_posterior_density() (gpflow.models.gpmc method)": [[21, "gpflow.models.GPMC.log_posterior_density"]], "log_posterior_density() (gpflow.models.sgpmc method)": [[21, "gpflow.models.SGPMC.log_posterior_density"]], "log_prior_density() (gpflow.models.bayesianmodel method)": [[21, "gpflow.models.BayesianModel.log_prior_density"]], "logdet_term() (gpflow.models.cglb method)": [[21, "gpflow.models.CGLB.logdet_term"]], "maximum_log_likelihood_objective() (gpflow.models.bayesiangplvm method)": [[21, "gpflow.models.BayesianGPLVM.maximum_log_likelihood_objective"]], "maximum_log_likelihood_objective() (gpflow.models.bayesianmodel method)": [[21, "gpflow.models.BayesianModel.maximum_log_likelihood_objective"]], "maximum_log_likelihood_objective() (gpflow.models.gpmc method)": [[21, "gpflow.models.GPMC.maximum_log_likelihood_objective"]], "maximum_log_likelihood_objective() (gpflow.models.gprfitc method)": [[21, "gpflow.models.GPRFITC.maximum_log_likelihood_objective"]], "maximum_log_likelihood_objective() (gpflow.models.sgpmc method)": [[21, "gpflow.models.SGPMC.maximum_log_likelihood_objective"]], "maximum_log_likelihood_objective() (gpflow.models.vgpopperarchambeau method)": [[21, "gpflow.models.VGPOpperArchambeau.maximum_log_likelihood_objective"]], "maximum_log_likelihood_objective() (in module gpflow.models)": [[21, "gpflow.models.maximum_log_likelihood_objective"]], "predict_f() (gpflow.models.bayesiangplvm method)": [[21, "gpflow.models.BayesianGPLVM.predict_f"]], "predict_f() (gpflow.models.cglb method)": [[21, "gpflow.models.CGLB.predict_f"]], "predict_f() (gpflow.models.gpmc method)": [[21, "gpflow.models.GPMC.predict_f"]], "predict_f() (gpflow.models.gpmodel method)": [[21, "gpflow.models.GPModel.predict_f"]], "predict_f() (gpflow.models.gprfitc method)": [[21, "gpflow.models.GPRFITC.predict_f"]], "predict_f() (gpflow.models.sgpmc method)": [[21, "gpflow.models.SGPMC.predict_f"]], "predict_f() (gpflow.models.vgpopperarchambeau method)": [[21, "gpflow.models.VGPOpperArchambeau.predict_f"]], "predict_f_samples() (gpflow.models.gpmodel method)": [[21, "gpflow.models.GPModel.predict_f_samples"]], "predict_log_density() (gpflow.models.bayesiangplvm method)": [[21, "gpflow.models.BayesianGPLVM.predict_log_density"]], "predict_log_density() (gpflow.models.cglb method)": [[21, "gpflow.models.CGLB.predict_log_density"]], "predict_log_density() (gpflow.models.gpmodel method)": [[21, "gpflow.models.GPModel.predict_log_density"]], "predict_y() (gpflow.models.cglb method)": [[21, "gpflow.models.CGLB.predict_y"]], "predict_y() (gpflow.models.gpmodel method)": [[21, "gpflow.models.GPModel.predict_y"]], "quad_term() (gpflow.models.cglb method)": [[21, "gpflow.models.CGLB.quad_term"]], "training_loss() (gpflow.models.externaldatatraininglossmixin method)": [[21, "gpflow.models.ExternalDataTrainingLossMixin.training_loss"]], "training_loss() (gpflow.models.internaldatatraininglossmixin method)": [[21, "gpflow.models.InternalDataTrainingLossMixin.training_loss"]], "training_loss() (in module gpflow.models)": [[21, "gpflow.models.training_loss"]], "training_loss_closure() (gpflow.models.externaldatatraininglossmixin method)": [[21, "gpflow.models.ExternalDataTrainingLossMixin.training_loss_closure"]], "training_loss_closure() (gpflow.models.internaldatatraininglossmixin method)": [[21, "gpflow.models.InternalDataTrainingLossMixin.training_loss_closure"]], "training_loss_closure() (in module gpflow.models)": [[21, "gpflow.models.training_loss_closure"]], "a (gpflow.models.sgpr.sgpr_deprecated.commontensors attribute)": [[22, "gpflow.models.sgpr.SGPR_deprecated.CommonTensors.A"]], "aat (gpflow.models.sgpr.sgpr_deprecated.commontensors attribute)": [[22, "gpflow.models.sgpr.SGPR_deprecated.CommonTensors.AAT"]], "b (gpflow.models.sgpr.sgpr_deprecated.commontensors attribute)": [[22, "gpflow.models.sgpr.SGPR_deprecated.CommonTensors.B"]], "l (gpflow.models.sgpr.sgpr_deprecated.commontensors attribute)": [[22, "gpflow.models.sgpr.SGPR_deprecated.CommonTensors.L"]], "lb (gpflow.models.sgpr.sgpr_deprecated.commontensors attribute)": [[22, "gpflow.models.sgpr.SGPR_deprecated.CommonTensors.LB"]], "sgprbase_deprecated (class in gpflow.models.sgpr)": [[22, "gpflow.models.sgpr.SGPRBase_deprecated"]], "sgpr_deprecated (class in gpflow.models.sgpr)": [[22, "gpflow.models.sgpr.SGPR_deprecated"]], "sgpr_deprecated.commontensors (class in gpflow.models.sgpr)": [[22, "gpflow.models.sgpr.SGPR_deprecated.CommonTensors"]], "sgpr_with_posterior (class in gpflow.models.sgpr)": [[22, "gpflow.models.sgpr.SGPR_with_posterior"]], "compute_qu() (gpflow.models.sgpr.sgpr_deprecated method)": [[22, "gpflow.models.sgpr.SGPR_deprecated.compute_qu"]], "elbo() (gpflow.models.sgpr.sgpr_deprecated method)": [[22, "gpflow.models.sgpr.SGPR_deprecated.elbo"]], "gpflow.models.sgpr": [[22, "module-gpflow.models.sgpr"]], "logdet_term() (gpflow.models.sgpr.sgpr_deprecated method)": [[22, "gpflow.models.sgpr.SGPR_deprecated.logdet_term"]], "maximum_log_likelihood_objective() (gpflow.models.sgpr.sgpr_deprecated method)": [[22, "gpflow.models.sgpr.SGPR_deprecated.maximum_log_likelihood_objective"]], "posterior() (gpflow.models.sgpr.sgpr_with_posterior method)": [[22, "gpflow.models.sgpr.SGPR_with_posterior.posterior"]], "predict_f() (gpflow.models.sgpr.sgpr_deprecated method)": [[22, "gpflow.models.sgpr.SGPR_deprecated.predict_f"]], "predict_f() (gpflow.models.sgpr.sgpr_with_posterior method)": [[22, "gpflow.models.sgpr.SGPR_with_posterior.predict_f"]], "quad_term() (gpflow.models.sgpr.sgpr_deprecated method)": [[22, "gpflow.models.sgpr.SGPR_deprecated.quad_term"]], "sigma (gpflow.models.sgpr.sgpr_deprecated.commontensors attribute)": [[22, "gpflow.models.sgpr.SGPR_deprecated.CommonTensors.sigma"]], "sigma_sq (gpflow.models.sgpr.sgpr_deprecated.commontensors attribute)": [[22, "gpflow.models.sgpr.SGPR_deprecated.CommonTensors.sigma_sq"]], "upper_bound() (gpflow.models.sgpr.sgprbase_deprecated method)": [[22, "gpflow.models.sgpr.SGPRBase_deprecated.upper_bound"]], "svgp_deprecated (class in gpflow.models.svgp)": [[23, "gpflow.models.svgp.SVGP_deprecated"]], "svgp_with_posterior (class in gpflow.models.svgp)": [[23, "gpflow.models.svgp.SVGP_with_posterior"]], "elbo() (gpflow.models.svgp.svgp_deprecated method)": [[23, "gpflow.models.svgp.SVGP_deprecated.elbo"]], "gpflow.models.svgp": [[23, "module-gpflow.models.svgp"]], "maximum_log_likelihood_objective() (gpflow.models.svgp.svgp_deprecated method)": [[23, "gpflow.models.svgp.SVGP_deprecated.maximum_log_likelihood_objective"]], "posterior() (gpflow.models.svgp.svgp_with_posterior method)": [[23, "gpflow.models.svgp.SVGP_with_posterior.posterior"]], "predict_f() (gpflow.models.svgp.svgp_deprecated method)": [[23, "gpflow.models.svgp.SVGP_deprecated.predict_f"]], "predict_f() (gpflow.models.svgp.svgp_with_posterior method)": [[23, "gpflow.models.svgp.SVGP_with_posterior.predict_f"]], "data_input_to_tensor() (in module gpflow.models.util)": [[24, "gpflow.models.util.data_input_to_tensor"]], "gpflow.models.util": [[24, "module-gpflow.models.util"]], "inducingpoint_wrapper() (in module gpflow.models.util)": [[24, "gpflow.models.util.inducingpoint_wrapper"]], "vgp_deprecated (class in gpflow.models.vgp)": [[25, "gpflow.models.vgp.VGP_deprecated"]], "vgp_with_posterior (class in gpflow.models.vgp)": [[25, "gpflow.models.vgp.VGP_with_posterior"]], "elbo() (gpflow.models.vgp.vgp_deprecated method)": [[25, "gpflow.models.vgp.VGP_deprecated.elbo"]], "gpflow.models.vgp": [[25, "module-gpflow.models.vgp"]], "maximum_log_likelihood_objective() (gpflow.models.vgp.vgp_deprecated method)": [[25, "gpflow.models.vgp.VGP_deprecated.maximum_log_likelihood_objective"]], "posterior() (gpflow.models.vgp.vgp_with_posterior method)": [[25, "gpflow.models.vgp.VGP_with_posterior.posterior"]], "predict_f() (gpflow.models.vgp.vgp_deprecated method)": [[25, "gpflow.models.vgp.VGP_deprecated.predict_f"]], "predict_f() (gpflow.models.vgp.vgp_with_posterior method)": [[25, "gpflow.models.vgp.VGP_with_posterior.predict_f"]], "update_vgp_data() (in module gpflow.models.vgp)": [[25, "gpflow.models.vgp.update_vgp_data"]], "executecallback (class in gpflow.monitor)": [[26, "gpflow.monitor.ExecuteCallback"]], "imagetotensorboard (class in gpflow.monitor)": [[26, "gpflow.monitor.ImageToTensorBoard"]], "modeltotensorboard (class in gpflow.monitor)": [[26, "gpflow.monitor.ModelToTensorBoard"]], "monitor (class in gpflow.monitor)": [[26, "gpflow.monitor.Monitor"]], "monitortask (class in gpflow.monitor)": [[26, "gpflow.monitor.MonitorTask"]], "monitortaskgroup (class in gpflow.monitor)": [[26, "gpflow.monitor.MonitorTaskGroup"]], "scalartotensorboard (class in gpflow.monitor)": [[26, "gpflow.monitor.ScalarToTensorBoard"]], "totensorboard (class in gpflow.monitor)": [[26, "gpflow.monitor.ToTensorBoard"]], "gpflow.monitor": [[26, "module-gpflow.monitor"]], "run() (gpflow.monitor.executecallback method)": [[26, "gpflow.monitor.ExecuteCallback.run"]], "run() (gpflow.monitor.imagetotensorboard method)": [[26, "gpflow.monitor.ImageToTensorBoard.run"]], "run() (gpflow.monitor.modeltotensorboard method)": [[26, "gpflow.monitor.ModelToTensorBoard.run"]], "run() (gpflow.monitor.monitortask method)": [[26, "gpflow.monitor.MonitorTask.run"]], "run() (gpflow.monitor.scalartotensorboard method)": [[26, "gpflow.monitor.ScalarToTensorBoard.run"]], "naturalgradient (class in gpflow.optimizers)": [[27, "gpflow.optimizers.NaturalGradient"]], "samplinghelper (class in gpflow.optimizers)": [[27, "gpflow.optimizers.SamplingHelper"]], "scipy (class in gpflow.optimizers)": [[27, "gpflow.optimizers.Scipy"]], "xinat (class in gpflow.optimizers)": [[27, "gpflow.optimizers.XiNat"]], "xisqrtmeanvar (class in gpflow.optimizers)": [[27, "gpflow.optimizers.XiSqrtMeanVar"]], "xitransform (class in gpflow.optimizers)": [[27, "gpflow.optimizers.XiTransform"]], "convert_to_constrained_values() (gpflow.optimizers.samplinghelper method)": [[27, "gpflow.optimizers.SamplingHelper.convert_to_constrained_values"]], "current_state (gpflow.optimizers.samplinghelper property)": [[27, "gpflow.optimizers.SamplingHelper.current_state"]], "get_config() (gpflow.optimizers.naturalgradient method)": [[27, "gpflow.optimizers.NaturalGradient.get_config"]], "gpflow.optimizers": [[27, "module-gpflow.optimizers"]], "meanvarsqrt_to_xi() (gpflow.optimizers.xinat static method)": [[27, "gpflow.optimizers.XiNat.meanvarsqrt_to_xi"]], "meanvarsqrt_to_xi() (gpflow.optimizers.xisqrtmeanvar static method)": [[27, "gpflow.optimizers.XiSqrtMeanVar.meanvarsqrt_to_xi"]], "meanvarsqrt_to_xi() (gpflow.optimizers.xitransform static method)": [[27, "gpflow.optimizers.XiTransform.meanvarsqrt_to_xi"]], "minimize() (gpflow.optimizers.naturalgradient method)": [[27, "gpflow.optimizers.NaturalGradient.minimize"]], "minimize() (gpflow.optimizers.scipy method)": [[27, "gpflow.optimizers.Scipy.minimize"]], "naturals_to_xi() (gpflow.optimizers.xinat static method)": [[27, "gpflow.optimizers.XiNat.naturals_to_xi"]], "naturals_to_xi() (gpflow.optimizers.xisqrtmeanvar static method)": [[27, "gpflow.optimizers.XiSqrtMeanVar.naturals_to_xi"]], "naturals_to_xi() (gpflow.optimizers.xitransform static method)": [[27, "gpflow.optimizers.XiTransform.naturals_to_xi"]], "target_log_prob_fn (gpflow.optimizers.samplinghelper property)": [[27, "gpflow.optimizers.SamplingHelper.target_log_prob_fn"]], "xi_to_meanvarsqrt() (gpflow.optimizers.xinat static method)": [[27, "gpflow.optimizers.XiNat.xi_to_meanvarsqrt"]], "xi_to_meanvarsqrt() (gpflow.optimizers.xisqrtmeanvar static method)": [[27, "gpflow.optimizers.XiSqrtMeanVar.xi_to_meanvarsqrt"]], "xi_to_meanvarsqrt() (gpflow.optimizers.xitransform static method)": [[27, "gpflow.optimizers.XiTransform.xi_to_meanvarsqrt"]], "expectation_to_meanvarsqrt() (in module gpflow.optimizers.natgrad)": [[28, "gpflow.optimizers.natgrad.expectation_to_meanvarsqrt"]], "expectation_to_natural() (in module gpflow.optimizers.natgrad)": [[28, "gpflow.optimizers.natgrad.expectation_to_natural"]], "gpflow.optimizers.natgrad": [[28, "module-gpflow.optimizers.natgrad"]], "meanvarsqrt_to_expectation() (in module gpflow.optimizers.natgrad)": [[28, "gpflow.optimizers.natgrad.meanvarsqrt_to_expectation"]], "meanvarsqrt_to_natural() (in module gpflow.optimizers.natgrad)": [[28, "gpflow.optimizers.natgrad.meanvarsqrt_to_natural"]], "natural_to_expectation() (in module gpflow.optimizers.natgrad)": [[28, "gpflow.optimizers.natgrad.natural_to_expectation"]], "natural_to_meanvarsqrt() (in module gpflow.optimizers.natgrad)": [[28, "gpflow.optimizers.natgrad.natural_to_meanvarsqrt"]], "swap_dimensions() (in module gpflow.optimizers.natgrad)": [[28, "gpflow.optimizers.natgrad.swap_dimensions"]], "abstractposterior (class in gpflow.posteriors)": [[29, "gpflow.posteriors.AbstractPosterior"]], "baseposterior (class in gpflow.posteriors)": [[29, "gpflow.posteriors.BasePosterior"]], "fallbackindependentlatentposterior (class in gpflow.posteriors)": [[29, "gpflow.posteriors.FallbackIndependentLatentPosterior"]], "fullycorrelatedposterior (class in gpflow.posteriors)": [[29, "gpflow.posteriors.FullyCorrelatedPosterior"]], "gprposterior (class in gpflow.posteriors)": [[29, "gpflow.posteriors.GPRPosterior"]], "independentposterior (class in gpflow.posteriors)": [[29, "gpflow.posteriors.IndependentPosterior"]], "independentposteriormultioutput (class in gpflow.posteriors)": [[29, "gpflow.posteriors.IndependentPosteriorMultiOutput"]], "independentposteriorsingleoutput (class in gpflow.posteriors)": [[29, "gpflow.posteriors.IndependentPosteriorSingleOutput"]], "linearcoregionalizationposterior (class in gpflow.posteriors)": [[29, "gpflow.posteriors.LinearCoregionalizationPosterior"]], "precomputecachetype (class in gpflow.posteriors)": [[29, "gpflow.posteriors.PrecomputeCacheType"]], "precomputedvalue (class in gpflow.posteriors)": [[29, "gpflow.posteriors.PrecomputedValue"]], "sgprposterior (class in gpflow.posteriors)": [[29, "gpflow.posteriors.SGPRPosterior"]], "vgpposterior (class in gpflow.posteriors)": [[29, "gpflow.posteriors.VGPPosterior"]], "_get_posterior_base_case() (in module gpflow.posteriors)": [[29, "gpflow.posteriors._get_posterior_base_case"]], "_get_posterior_fully_correlated_mo() (in module gpflow.posteriors)": [[29, "gpflow.posteriors._get_posterior_fully_correlated_mo"]], "_get_posterior_independent_mo() (in module gpflow.posteriors)": [[29, "gpflow.posteriors._get_posterior_independent_mo"]], "_get_posterior_independentlatent_mo_fallback() (in module gpflow.posteriors)": [[29, "gpflow.posteriors._get_posterior_independentlatent_mo_fallback"]], "_get_posterior_linearcoregionalization_mo_efficient() (in module gpflow.posteriors)": [[29, "gpflow.posteriors._get_posterior_linearcoregionalization_mo_efficient"]], "axis_dynamic (gpflow.posteriors.precomputedvalue attribute)": [[29, "gpflow.posteriors.PrecomputedValue.axis_dynamic"]], "create_posterior() (in module gpflow.posteriors)": [[29, "gpflow.posteriors.create_posterior"]], "fused_predict_f() (gpflow.posteriors.abstractposterior method)": [[29, "gpflow.posteriors.AbstractPosterior.fused_predict_f"]], "get_precomputed_value_shape() (in module gpflow.posteriors)": [[29, "gpflow.posteriors.get_precomputed_value_shape"]], "gpflow.posteriors": [[29, "module-gpflow.posteriors"]], "predict_f() (gpflow.posteriors.abstractposterior method)": [[29, "gpflow.posteriors.AbstractPosterior.predict_f"]], "update_cache() (gpflow.posteriors.abstractposterior method)": [[29, "gpflow.posteriors.AbstractPosterior.update_cache"]], "value (gpflow.posteriors.precomputedvalue attribute)": [[29, "gpflow.posteriors.PrecomputedValue.value"]], "wrap_alpha_qinv() (gpflow.posteriors.precomputedvalue static method)": [[29, "gpflow.posteriors.PrecomputedValue.wrap_alpha_Qinv"]], "diagonalgaussian (class in gpflow.probability_distributions)": [[30, "gpflow.probability_distributions.DiagonalGaussian"]], "gaussian (class in gpflow.probability_distributions)": [[30, "gpflow.probability_distributions.Gaussian"]], "markovgaussian (class in gpflow.probability_distributions)": [[30, "gpflow.probability_distributions.MarkovGaussian"]], "probabilitydistribution (class in gpflow.probability_distributions)": [[30, "gpflow.probability_distributions.ProbabilityDistribution"]], "get_probability_distribution_shape() (in module gpflow.probability_distributions)": [[30, "gpflow.probability_distributions.get_probability_distribution_shape"]], "gpflow.probability_distributions": [[30, "module-gpflow.probability_distributions"]], "shape (gpflow.probability_distributions.diagonalgaussian property)": [[30, "gpflow.probability_distributions.DiagonalGaussian.shape"]], "shape (gpflow.probability_distributions.gaussian property)": [[30, "gpflow.probability_distributions.Gaussian.shape"]], "shape (gpflow.probability_distributions.markovgaussian property)": [[30, "gpflow.probability_distributions.MarkovGaussian.shape"]], "shape (gpflow.probability_distributions.probabilitydistribution property)": [[30, "gpflow.probability_distributions.ProbabilityDistribution.shape"]], "gh_points_and_weights() (in module gpflow.quadrature.gauss_hermite)": [[31, "gpflow.quadrature.gauss_hermite.gh_points_and_weights"]], "gpflow.quadrature.gauss_hermite": [[31, "module-gpflow.quadrature.gauss_hermite"]], "list_to_flat_grid() (in module gpflow.quadrature.gauss_hermite)": [[31, "gpflow.quadrature.gauss_hermite.list_to_flat_grid"]], "ndgh_points_and_weights() (in module gpflow.quadrature.gauss_hermite)": [[31, "gpflow.quadrature.gauss_hermite.ndgh_points_and_weights"]], "repeat_as_list() (in module gpflow.quadrature.gauss_hermite)": [[31, "gpflow.quadrature.gauss_hermite.repeat_as_list"]], "reshape_z_dz() (in module gpflow.quadrature.gauss_hermite)": [[31, "gpflow.quadrature.gauss_hermite.reshape_Z_dZ"]], "gaussianquadrature (class in gpflow.quadrature)": [[32, "gpflow.quadrature.GaussianQuadrature"]], "ndiagghquadrature (class in gpflow.quadrature)": [[32, "gpflow.quadrature.NDiagGHQuadrature"]], "gpflow.quadrature": [[32, "module-gpflow.quadrature"]], "hermgauss() (in module gpflow.quadrature)": [[32, "gpflow.quadrature.hermgauss"]], "logspace() (gpflow.quadrature.gaussianquadrature method)": [[32, "gpflow.quadrature.GaussianQuadrature.logspace"]], "mvhermgauss() (in module gpflow.quadrature)": [[32, "gpflow.quadrature.mvhermgauss"]], "mvnquad() (in module gpflow.quadrature)": [[32, "gpflow.quadrature.mvnquad"]], "ndiag_mc() (in module gpflow.quadrature)": [[32, "gpflow.quadrature.ndiag_mc"]], "ndiagquad() (in module gpflow.quadrature)": [[32, "gpflow.quadrature.ndiagquad"]], "compute_mypy_flags() (in module gpflow.type_flags)": [[33, "gpflow.type_flags.compute_mypy_flags"]], "gpflow.type_flags": [[33, "module-gpflow.type_flags"]], "dispatcher (class in gpflow.utilities)": [[34, "gpflow.utilities.Dispatcher"]], "add_likelihood_noise_cov() (in module gpflow.utilities)": [[34, "gpflow.utilities.add_likelihood_noise_cov"]], "add_noise_cov() (in module gpflow.utilities)": [[34, "gpflow.utilities.add_noise_cov"]], "assert_params_false() (in module gpflow.utilities)": [[34, "gpflow.utilities.assert_params_false"]], "deepcopy() (in module gpflow.utilities)": [[34, "gpflow.utilities.deepcopy"]], "dispatch() (gpflow.utilities.dispatcher method)": [[34, "gpflow.utilities.Dispatcher.dispatch"]], "dispatch_or_raise() (gpflow.utilities.dispatcher method)": [[34, "gpflow.utilities.Dispatcher.dispatch_or_raise"]], "freeze() (in module gpflow.utilities)": [[34, "gpflow.utilities.freeze"]], "get_first_occurrence() (gpflow.utilities.dispatcher method)": [[34, "gpflow.utilities.Dispatcher.get_first_occurrence"]], "gpflow.utilities": [[34, "module-gpflow.utilities"]], "is_variable() (in module gpflow.utilities)": [[34, "gpflow.utilities.is_variable"]], "leaf_components() (in module gpflow.utilities)": [[34, "gpflow.utilities.leaf_components"]], "multiple_assign() (in module gpflow.utilities)": [[34, "gpflow.utilities.multiple_assign"]], "parameter_dict() (in module gpflow.utilities)": [[34, "gpflow.utilities.parameter_dict"]], "positive() (in module gpflow.utilities)": [[34, "gpflow.utilities.positive"]], "print_summary() (in module gpflow.utilities)": [[34, "gpflow.utilities.print_summary"]], "read_values() (in module gpflow.utilities)": [[34, "gpflow.utilities.read_values"]], "register() (gpflow.utilities.dispatcher method)": [[34, "gpflow.utilities.Dispatcher.register"]], "reset_cache_bijectors() (in module gpflow.utilities)": [[34, "gpflow.utilities.reset_cache_bijectors"]], "select_dict_parameters_with_prior() (in module gpflow.utilities)": [[34, "gpflow.utilities.select_dict_parameters_with_prior"]], "tabulate_module_summary() (in module gpflow.utilities)": [[34, "gpflow.utilities.tabulate_module_summary"]], "to_default_float() (in module gpflow.utilities)": [[34, "gpflow.utilities.to_default_float"]], "to_default_int() (in module gpflow.utilities)": [[34, "gpflow.utilities.to_default_int"]], "training_loop() (in module gpflow.utilities)": [[34, "gpflow.utilities.training_loop"]], "traverse_module() (in module gpflow.utilities)": [[34, "gpflow.utilities.traverse_module"]], "triangular() (in module gpflow.utilities)": [[34, "gpflow.utilities.triangular"]], "triangular_size() (in module gpflow.utilities)": [[34, "gpflow.utilities.triangular_size"]], "broadcasting_elementwise() (in module gpflow.utilities.ops)": [[35, "gpflow.utilities.ops.broadcasting_elementwise"]], "difference_matrix() (in module gpflow.utilities.ops)": [[35, "gpflow.utilities.ops.difference_matrix"]], "eye() (in module gpflow.utilities.ops)": [[35, "gpflow.utilities.ops.eye"]], "gpflow.utilities.ops": [[35, "module-gpflow.utilities.ops"]], "leading_transpose() (in module gpflow.utilities.ops)": [[35, "gpflow.utilities.ops.leading_transpose"]], "pca_reduce() (in module gpflow.utilities.ops)": [[35, "gpflow.utilities.ops.pca_reduce"]], "square_distance() (in module gpflow.utilities.ops)": [[35, "gpflow.utilities.ops.square_distance"]], "evaluate_parameter_or_function() (in module gpflow.utilities.parameter_or_function)": [[36, "gpflow.utilities.parameter_or_function.evaluate_parameter_or_function"]], "gpflow.utilities.parameter_or_function": [[36, "module-gpflow.utilities.parameter_or_function"]], "prepare_parameter_or_function() (in module gpflow.utilities.parameter_or_function)": [[36, "gpflow.utilities.parameter_or_function.prepare_parameter_or_function"]]}})