probability_distributions.py

```
# Copyright 2017-2020 The GPflow Contributors. All Rights Reserved.
#
# 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
# probability distributions. The TensorFlow "distributions" framework would
# be a good replacement.
from .base import TensorType
class ProbabilityDistribution:
"""
This is the base class for a probability distributions,
over which we take the expectations in the expectations framework.
"""
class Gaussian(ProbabilityDistribution):
def __init__(self, mu: TensorType, cov: TensorType):
self.mu = mu # [N, D]
self.cov = cov # [N, D, D]
class DiagonalGaussian(ProbabilityDistribution):
def __init__(self, mu: TensorType, cov: TensorType):
self.mu = mu # [N, D]
self.cov = cov # [N, 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: TensorType, cov: TensorType):
self.mu = mu # N+[1, D]
self.cov = cov # 2 x (N+1)[, D, D]
```