# Copyright 2016 the GPflow authors. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License.from __future__ import print_function import tensorflow as tf import numpy as np from numpy.testing import assert_allclose import gpflow from gpflow.test_util import GPflowTestCase class TestEquivalence(GPflowTestCase): """ With a Gaussian likelihood, and inducing points (where appropriate) positioned at the data, many of the gpflow methods are equivalent (perhaps subject to some optimization). Here, we make 5 models that should be the same, and make sure some similarites hold. The models are: 1) GP Regression 2) Variational GP (with the likelihood set to Gaussian) 3) Sparse variational GP (likelihood is Gaussian, inducing points at the data) 4) Sparse variational GP (as above, but with the whitening rotation of the inducing variables) 5) Sparse variational GP Regression (as above, but there the inducing variables are 'collapsed' out, as in Titsias 2009) """ def prepare(self): rng = np.random.RandomState(0) X = rng.rand(20, 1) * 10 Y = np.sin(X) + 0.9 * np.cos(X * 1.6) + rng.randn(*X.shape) * 0.8 Y = np.tile(Y, 2) # two identical columns self.Xtest = rng.rand(10, 1) * 10 m1 = gpflow.models.GPR( X, Y, kern=gpflow.kernels.RBF(1), mean_function=gpflow.mean_functions.Constant()) m2 = gpflow.models.VGP( X, Y, gpflow.kernels.RBF(1), likelihood=gpflow.likelihoods.Gaussian(), mean_function=gpflow.mean_functions.Constant()) m3 = gpflow.models.SVGP( X, Y, gpflow.kernels.RBF(1), likelihood=gpflow.likelihoods.Gaussian(), Z=X.copy(), q_diag=False, mean_function=gpflow.mean_functions.Constant()) m3.feature.trainable = False m4 = gpflow.models.SVGP( X, Y, gpflow.kernels.RBF(1), likelihood=gpflow.likelihoods.Gaussian(), Z=X.copy(), q_diag=False, whiten=True, mean_function=gpflow.mean_functions.Constant()) m4.feature.trainable = False m5 = gpflow.models.SGPR( X, Y, gpflow.kernels.RBF(1), Z=X.copy(), mean_function=gpflow.mean_functions.Constant()) m5.feature.trainable = False m6 = gpflow.models.GPRFITC( X, Y, gpflow.kernels.RBF(1), Z=X.copy(), mean_function=gpflow.mean_functions.Constant()) m6.feature.trainable = False return [m1, m2, m3, m4, m5, m6] def test_all(self): with self.test_context() as session: models = self.prepare() likelihoods = [] for m in models: opt = gpflow.train.ScipyOptimizer() opt.minimize(m, maxiter=300) neg_obj = tf.negative(m.objective) likelihoods.append(session.run(neg_obj).squeeze()) assert_allclose(likelihoods, likelihoods[0], rtol=1e-6) variances, lengthscales = [], [] for m in models: if hasattr(m.kern, 'rbf'): variances.append(m.kern.rbf.variance.read_value()) lengthscales.append(m.kern.rbf.lengthscales.read_value()) else: variances.append(m.kern.variance.read_value()) lengthscales.append(m.kern.lengthscales.read_value()) variances, lengthscales = np.array(variances), np.array(lengthscales) assert_allclose(variances, variances[0], 1e-5) assert_allclose(lengthscales, lengthscales.mean(), 1e-4) mu0, var0 = models[0].predict_y(self.Xtest) for m in models[1:]: mu, var = m.predict_y(self.Xtest) assert_allclose(mu, mu0, 1e-3) assert_allclose(var, var0, 1e-4) class VGPTest(GPflowTestCase): def test_vgp_vs_svgp(self): with self.test_context(): N, Ns, DX, DY = 100, 10, 2, 2 np.random.seed(1) X = np.random.randn(N, DX) Xs = np.random.randn(Ns, DX) Y = np.random.randn(N, DY) kern = gpflow.kernels.Matern52(DX) likelihood = gpflow.likelihoods.StudentT() m_svgp = gpflow.models.SVGP( X, Y, kern, likelihood, X.copy(), whiten=True, q_diag=False) m_vgp = gpflow.models.VGP(X, Y, kern, likelihood) m_svgp.compile() m_vgp.compile() q_mu = np.random.randn(N, DY) q_sqrt = np.random.randn(DY, N, N) m_svgp.q_mu = q_mu m_svgp.q_sqrt = q_sqrt m_vgp.q_mu = q_mu m_vgp.q_sqrt = q_sqrt L_svgp = m_svgp.compute_log_likelihood() L_vgp = m_vgp.compute_log_likelihood() assert_allclose(L_svgp, L_vgp, rtol=1e-2) pred_svgp = m_svgp.predict_f(Xs) pred_vgp = m_vgp.predict_f(Xs) assert_allclose(pred_svgp[0], pred_vgp[0]) assert_allclose(pred_svgp[1], pred_vgp[1]) def test_vgp_vs_opper_archambeau(self): with self.test_context(): N, Ns, DX, DY = 100, 10, 2, 2 np.random.seed(1) X = np.random.randn(N, DX) Xs = np.random.randn(Ns, DX) Y = np.random.randn(N, DY) kern = gpflow.kernels.Matern52(DX) likelihood = gpflow.likelihoods.StudentT() m_vgp = gpflow.models.VGP(X, Y, kern, likelihood) m_vgp_oa = gpflow.models.VGP_opper_archambeau(X, Y, kern, likelihood) m_vgp.compile() m_vgp_oa.compile() q_alpha = np.random.randn(N, DX) q_lambda = np.random.randn(N, DX) ** 2 m_vgp_oa.q_alpha = q_alpha m_vgp_oa.q_lambda = q_lambda K = kern.compute_K_symm(X) + np.eye(N) * gpflow.settings.jitter L = np.linalg.cholesky(K) L_inv = np.linalg.inv(L) K_inv = np.linalg.inv(K) mean = K.dot(q_alpha) prec_dnn = K_inv[None, :, :] + np.array([np.diag(l ** 2) for l in q_lambda.T]) var_dnn = np.linalg.inv(prec_dnn) m_svgp_unwhitened = gpflow.models.SVGP( X, Y, kern, likelihood, X.copy(), whiten=False, q_diag=False) m_svgp_unwhitened.q_mu = mean m_svgp_unwhitened.q_sqrt = np.linalg.cholesky(var_dnn) m_svgp_unwhitened.compile() mean_white_nd = L_inv.dot(mean) var_white_dnn = np.einsum('nN,dNM,mM->dnm', L_inv, var_dnn, L_inv) q_sqrt_nnd = np.linalg.cholesky(var_white_dnn) m_vgp.q_mu = mean_white_nd m_vgp.q_sqrt = q_sqrt_nnd L_vgp = m_vgp.compute_log_likelihood() L_svgp_unwhitened = m_svgp_unwhitened.compute_log_likelihood() L_vgp_oa = m_vgp_oa.compute_log_likelihood() assert_allclose(L_vgp, L_vgp_oa, rtol=1e-2) assert_allclose(L_vgp, L_svgp_unwhitened, rtol=1e-2) pred_vgp = m_vgp.predict_f(Xs) pred_svgp_unwhitened = m_svgp_unwhitened.predict_f(Xs) pred_vgp_oa = m_vgp_oa.predict_f(Xs) assert_allclose(pred_vgp[0], pred_vgp_oa[0]) assert_allclose(pred_vgp[0], pred_svgp_unwhitened[0]) assert_allclose(pred_vgp[1], pred_vgp_oa[1], rtol=1e-4) # jitter? assert_allclose(pred_vgp[1], pred_svgp_unwhitened[1], rtol=1e-4) #def test_recompile(self): # with self.test_context(): # N, DX, DY = 100, 2, 2 # np.random.seed(1) # X = np.random.randn(N, DX) # Y = np.random.randn(N, DY) # kern = gpflow.kernels.Matern52(DX) # likelihood = gpflow.likelihoods.StudentT() # m_vgp = gpflow.models.VGP(X, Y, kern, likelihood) # m_vgp_oa = gpflow.models.VGP_opper_archambeau(X, Y, kern, likelihood) # for m in [m_vgp, m_vgp_oa]: # m.compile() # opt = gpflow.train.ScipyOptimizer() # opt.minimize(m, maxiter=1) # m.X = X[:-1, :] # m.Y = Y[:-1, :] # opt.minimize(m, maxiter=1) class TestUpperBound(GPflowTestCase): """ Test for upper bound for regression marginal likelihood """ def setUp(self): self.X = np.random.rand(100, 1) self.Y = np.sin(1.5 * 2 * np.pi * self.X) + np.random.randn(*self.X.shape) * 0.1 def test_few_inducing_points(self): with self.test_context() as session: vfe = gpflow.models.SGPR(self.X, self.Y, gpflow.kernels.RBF(1), self.X[:10, :].copy()) opt = gpflow.train.ScipyOptimizer() opt.minimize(vfe) full = gpflow.models.GPR(self.X, self.Y, gpflow.kernels.RBF(1)) full.kern.lengthscales = vfe.kern.lengthscales.read_value() full.kern.variance = vfe.kern.variance.read_value() full.likelihood.variance = vfe.likelihood.variance.read_value() lml_upper = vfe.compute_upper_bound() lml_vfe = - session.run(vfe.objective) lml_full = - session.run(full.objective) self.assertTrue(lml_upper > lml_full > lml_vfe) if __name__ == '__main__': tf.test.main()