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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 from .. import settings from ..params import Parameter, DataHolder from ..decors import params_as_tensors from ..priors import Gaussian from ..conditionals import conditional from .model import GPModel class GPMC(GPModel): def __init__(self, X, Y, kern, likelihood, mean_function=None, num_latent=None, **kwargs): """ X is a data matrix, size N x D Y is a data matrix, size N x R kern, 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 """ X = DataHolder(X) Y = DataHolder(Y) GPModel.__init__(self, X, Y, kern, 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 = Gaussian(0., 1.) def compile(self, session=None): """ Before calling the standard compile function, check to see if the size of the data has changed and add parameters appropriately. This is necessary because the shape of the parameters depends on the shape of the data. """ if not self.num_data == self.X.shape: self.num_data = self.X.shape self.V = Parameter(np.zeros((self.num_data, self.num_latent))) self.V.prior = Gaussian(0., 1.) return super(GPMC, self).compile(session=session) @params_as_tensors def _build_likelihood(self): r""" Construct a tf function to compute the likelihood of a general GP model. \log p(Y, V | theta). """ K = self.kern.K(self.X) L = tf.cholesky( K + tf.eye(tf.shape(self.X), dtype=settings.float_type) * settings.numerics.jitter_level) F = tf.matmul(L, self.V) + self.mean_function(self.X) return tf.reduce_sum(self.likelihood.logp(F, self.Y)) @params_as_tensors def _build_predict(self, Xnew, full_cov=False): """ 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.kern, self.V, full_cov=full_cov, q_sqrt=None, white=True) return mu + self.mean_function(Xnew), var