# 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.
from functools import reduce
from typing import Type
import tensorflow as tf
from .. import kernels
from ..inducing_variables import InducingPoints
from ..probability_distributions import DiagonalGaussian
from . import dispatch
from .expectations import expectation
NoneType: Type[None] = type(None)
@dispatch.expectation.register(DiagonalGaussian, kernels.Product, NoneType, NoneType, NoneType)
def _expectation_diagonal_product(
p: DiagonalGaussian, kernel: kernels.Product, _: None, __: None, ___: None, nghp: None = None
) -> tf.Tensor:
r"""
Compute the expectation:
<\HadamardProd_i diag(Ki_{X[:, active_dims_i], X[:, active_dims_i]})>_p(X)
- \HadamardProd_i Ki_{.,.} :: Product kernel
- p :: DiagonalGaussian distribution (p.cov NxD)
:return: N
"""
if not kernel.on_separate_dimensions:
raise NotImplementedError(
"Product currently needs to be defined on separate dimensions."
) # pragma: no cover
exps = [expectation(p, k, nghp=nghp) for k in kernel.kernels]
return reduce(tf.multiply, exps)
@dispatch.expectation.register(
DiagonalGaussian, kernels.Product, InducingPoints, NoneType, NoneType
)
def _expectation_diagonal_product_inducingpoints(
p: DiagonalGaussian,
kernel: kernels.Product,
inducing_variable: InducingPoints,
__: None,
___: None,
nghp: None = None,
) -> tf.Tensor:
r"""
Compute the expectation:
<\HadamardProd_i Ki_{X[:, active_dims_i], Z[:, active_dims_i]}>_p(X)
- \HadamardProd_i Ki_{.,.} :: Product kernel
- p :: DiagonalGaussian distribution (p.cov NxD)
:return: NxM
"""
if not kernel.on_separate_dimensions:
raise NotImplementedError(
"Product currently needs to be defined on separate dimensions."
) # pragma: no cover
exps = [expectation(p, (k, inducing_variable), nghp=nghp) for k in kernel.kernels]
return reduce(tf.multiply, exps)
@dispatch.expectation.register(
DiagonalGaussian, kernels.Product, InducingPoints, kernels.Product, InducingPoints
)
def _expectation_diagonal_product_inducingpoints__product_inducingpoints(
p: DiagonalGaussian,
kern1: kernels.Product,
feat1: InducingPoints,
kern2: kernels.Product,
feat2: InducingPoints,
nghp: None = None,
) -> tf.Tensor:
r"""
Compute the expectation:
expectation[n] = < prodK_{Z, x_n} prodK_{x_n, Z} >_p(x_n)
= < (\HadamardProd_i Ki_{Z[:, active_dims_i], x[n, active_dims_i]}) <-- Mx1
1xM --> (\HadamardProd_j Kj_{x[n, active_dims_j], Z[:, active_dims_j]}) >_p(x_n) (MxM)
- \HadamardProd_i Ki_{.,.}, \HadamardProd_j Kj_{.,.} :: Product kernels
- p :: DiagonalGaussian distribution (p.cov NxD)
:return: NxMxM
"""
if feat1 != feat2:
raise NotImplementedError("Different inducing variables are not supported.")
if kern1 != kern2:
raise NotImplementedError(
"Calculating the expectation over two " "different Product kernels is not supported."
)
kernel = kern1
inducing_variable = feat1
if not kernel.on_separate_dimensions:
raise NotImplementedError(
"Product currently needs to be defined on separate dimensions."
) # pragma: no cover
exps = [
expectation(p, (k, inducing_variable), (k, inducing_variable), nghp=nghp)
for k in kernel.kernels
]
return reduce(tf.multiply, exps)