Revision

**8e64ed039275cf1d3b66856277023c9548317bd8**authored by Jesper Nielsen on**11 April 2022, 09:22:07 UTC**, committed by GitHub on**11 April 2022, 09:22:07 UTC****1 parent**3f74b5c

sums.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.
import itertools
from functools import reduce
from typing import Type, Union
import tensorflow as tf
from .. import kernels
from .. import mean_functions as mfn
from ..inducing_variables import InducingPoints
from ..probability_distributions import DiagonalGaussian, Gaussian, MarkovGaussian
from . import dispatch
from .expectations import expectation
NoneType: Type[None] = type(None)
@dispatch.expectation.register(Gaussian, kernels.Sum, NoneType, NoneType, NoneType)
def _expectation_gaussian_sum(
p: Gaussian, kernel: kernels.Sum, _: None, __: None, ___: None, nghp: None = None
) -> tf.Tensor:
r"""
Compute the expectation:
<\Sum_i diag(Ki_{X, X})>_p(X)
- \Sum_i Ki_{.,.} :: Sum kernel
:return: N
"""
exps = [expectation(p, k, nghp=nghp) for k in kernel.kernels]
return reduce(tf.add, exps)
@dispatch.expectation.register(Gaussian, kernels.Sum, InducingPoints, NoneType, NoneType)
def _expectation_gaussian_sum_inducingpoints(
p: Gaussian,
kernel: kernels.Sum,
inducing_variable: InducingPoints,
_: None,
__: None,
nghp: None = None,
) -> tf.Tensor:
r"""
Compute the expectation:
<\Sum_i Ki_{X, Z}>_p(X)
- \Sum_i Ki_{.,.} :: Sum kernel
:return: NxM
"""
exps = [expectation(p, (k, inducing_variable), nghp=nghp) for k in kernel.kernels]
return reduce(tf.add, exps)
@dispatch.expectation.register(
Gaussian, (mfn.Linear, mfn.Identity, mfn.Constant), NoneType, kernels.Sum, InducingPoints
)
def _expectation_gaussian_linear__sum_inducingpoints(
p: Gaussian,
mean: Union[mfn.Linear, mfn.Identity, mfn.Constant],
_: None,
kernel: kernels.Sum,
inducing_variable: InducingPoints,
nghp: None = None,
) -> tf.Tensor:
r"""
Compute the expectation:
expectation[n] = <m(x_n)^T (\Sum_i Ki_{x_n, Z})>_p(x_n)
- \Sum_i Ki_{.,.} :: Sum kernel
:return: NxQxM
"""
exps = [expectation(p, mean, (k, inducing_variable), nghp=nghp) for k in kernel.kernels]
return reduce(tf.add, exps)
@dispatch.expectation.register(MarkovGaussian, mfn.Identity, NoneType, kernels.Sum, InducingPoints)
def _expectation_markov__sum_inducingpoints(
p: MarkovGaussian,
mean: mfn.Identity,
_: None,
kernel: kernels.Sum,
inducing_variable: InducingPoints,
nghp: None = None,
) -> tf.Tensor:
r"""
Compute the expectation:
expectation[n] = <x_{n+1} (\Sum_i Ki_{x_n, Z})>_p(x_{n:n+1})
- \Sum_i Ki_{.,.} :: Sum kernel
:return: NxDxM
"""
exps = [expectation(p, mean, (k, inducing_variable), nghp=nghp) for k in kernel.kernels]
return reduce(tf.add, exps)
@dispatch.expectation.register(
(Gaussian, DiagonalGaussian), kernels.Sum, InducingPoints, kernels.Sum, InducingPoints
)
def _expectation_gaussian_sum_inducingpoints__sum_inducingpoints(
p: Union[Gaussian, DiagonalGaussian],
kern1: kernels.Sum,
feat1: InducingPoints,
kern2: kernels.Sum,
feat2: InducingPoints,
nghp: None = None,
) -> tf.Tensor:
r"""
Compute the expectation:
expectation[n] = <(\Sum_i K1_i_{Z1, x_n}) (\Sum_j K2_j_{x_n, Z2})>_p(x_n)
- \Sum_i K1_i_{.,.}, \Sum_j K2_j_{.,.} :: Sum kernels
:return: NxM1xM2
"""
crossexps = []
if kern1 == kern2 and feat1 == feat2: # avoid duplicate computation by using transposes
for i, k1 in enumerate(kern1.kernels):
crossexps.append(expectation(p, (k1, feat1), (k1, feat1), nghp=nghp))
for k2 in kern1.kernels[:i]:
eKK = expectation(p, (k1, feat1), (k2, feat2), nghp=nghp)
eKK += tf.linalg.adjoint(eKK)
crossexps.append(eKK)
else:
for k1, k2 in itertools.product(kern1.kernels, kern2.kernels):
crossexps.append(expectation(p, (k1, feat1), (k2, feat2), nghp=nghp))
return reduce(tf.add, crossexps)
```

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