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# Copyright 2016 James Hensman, alexggmatthews # # 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. import numpy as np import tensorflow as tf import tensorflow_probability as tfp from gpflow.base import Parameter from gpflow.config import default_float, default_jitter from ..conditionals import conditional from .model import GPModelOLD, MeanAndVariance class GPMC(GPModelOLD): def __init__(self, X, Y, kernel, likelihood, mean_function=None, num_latent=None, **kwargs): """ X is a data matrix, size [N, D] Y is a data matrix, size [N, R] kernel, likelihood, mean_function are appropriate GPflow objects This is a vanilla implementation of a GP with a non-Gaussian likelihood. The latent function values are represented by centered (whitened) variables, so v ~ N(0, I) f = Lv + m(x) with L L^T = K """ GPModelOLD.__init__(self, X, Y, kernel, likelihood, mean_function, num_latent, **kwargs) self.num_data = X.shape self.V = Parameter(np.zeros((self.num_data, self.num_latent))) self.V.prior = tfp.distributions.Normal(loc=0., scale=1.) def log_likelihood(self, *args, **kwargs) -> tf.Tensor: """ Construct a tf function to compute the likelihood of a general GP model. \log p(Y, V | theta). """ K = self.kernel(self.X) L = tf.linalg.cholesky( K + tf.eye(tf.shape(self.X), dtype=default_float()) * default_jitter()) F = tf.linalg.matmul(L, self.V) + self.mean_function(self.X) return tf.reduce_sum(self.likelihood.log_prob(F, self.Y)) def predict_f(self, Xnew: tf.Tensor, full_cov=False, full_output_cov=False) -> MeanAndVariance: """ Xnew is a data matrix, point at which we want to predict This method computes p(F* | (F=LV) ) where F* are points on the GP at Xnew, F=LV are points on the GP at X. """ mu, var = conditional(Xnew, self.X, self.kernel, self.V, full_cov=full_cov, q_sqrt=None, white=True) return mu + self.mean_function(Xnew), var