# Copyright 2017 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. # Eventually, it would be nice to not have to have our own classes for # proability distributions. The TensorFlow "distributions" framework would # be a good replacement. class ProbabilityDistribution: """ This is the base class for a probability distributions, over which we take the expectations in the expectations framework. """ pass class Gaussian(ProbabilityDistribution): def __init__(self, mu, cov): self.mu = mu # N x D self.cov = cov # N x D x D class DiagonalGaussian(ProbabilityDistribution): def __init__(self, mu, cov): self.mu = mu # N x D self.cov = cov # N x D class MarkovGaussian(ProbabilityDistribution): """ Gaussian distribution with Markov structure. Only covariances and covariances between t and t+1 need to be parameterised. We use the solution proposed by Carl Rasmussen, i.e. to represent Var[x_t] = cov[x_t, :, :] * cov[x_t, :, :].T Cov[x_t, x_{t+1}] = cov[t, :, :] * cov[t+1, :, :] """ def __init__(self, mu, cov): self.mu = mu # N+1 x D self.cov = cov # 2 x (N+1) x D x D