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

linears.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.
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.Linear, NoneType, NoneType, NoneType)
def _expectation_gaussian_linear(
p: Gaussian, kernel: kernels.Linear, _: None, __: None, ___: None, nghp: None = None
) -> tf.Tensor:
"""
Compute the expectation:
<diag(K_{X, X})>_p(X)
- K_{.,.} :: Linear kernel
:return: N
"""
# use only active dimensions
Xmu, _ = kernel.slice(p.mu, None)
Xcov = kernel.slice_cov(p.cov)
return tf.reduce_sum(kernel.variance * (tf.linalg.diag_part(Xcov) + Xmu ** 2), 1)
@dispatch.expectation.register(Gaussian, kernels.Linear, InducingPoints, NoneType, NoneType)
def _expectation_gaussian_linear_inducingpoints(
p: Gaussian,
kernel: kernels.Linear,
inducing_variable: InducingPoints,
_: None,
__: None,
nghp: None = None,
) -> tf.Tensor:
"""
Compute the expectation:
<K_{X, Z}>_p(X)
- K_{.,.} :: Linear kernel
:return: NxM
"""
# use only active dimensions
Z, Xmu = kernel.slice(inducing_variable.Z, p.mu)
return tf.linalg.matmul(Xmu, Z * kernel.variance, transpose_b=True)
@dispatch.expectation.register(Gaussian, kernels.Linear, InducingPoints, mfn.Identity, NoneType)
def _expectation_gaussian_linear_inducingpoints__identity(
p: Gaussian,
kernel: kernels.Linear,
inducing_variable: InducingPoints,
mean: mfn.Identity,
_: None,
nghp: None = None,
) -> tf.Tensor:
"""
Compute the expectation:
expectation[n] = <K_{Z, x_n} x_n^T>_p(x_n)
- K_{.,.} :: Linear kernel
:return: NxMxD
"""
Xmu, Xcov = p.mu, p.cov
N = tf.shape(Xmu)[0]
var_Z = kernel.variance * inducing_variable.Z # MxD
tiled_Z = tf.tile(tf.expand_dims(var_Z, 0), (N, 1, 1)) # NxMxD
return tf.linalg.matmul(tiled_Z, Xcov + (Xmu[..., None] * Xmu[:, None, :]))
@dispatch.expectation.register(
MarkovGaussian, kernels.Linear, InducingPoints, mfn.Identity, NoneType
)
def _expectation_markov_linear_inducingpoints__identity(
p: MarkovGaussian,
kernel: kernels.Linear,
inducing_variable: InducingPoints,
mean: mfn.Identity,
_: None,
nghp: None = None,
) -> tf.Tensor:
"""
Compute the expectation:
expectation[n] = <K_{Z, x_n} x_{n+1}^T>_p(x_{n:n+1})
- K_{.,.} :: Linear kernel
- p :: MarkovGaussian distribution (p.cov 2x(N+1)xDxD)
:return: NxMxD
"""
Xmu, Xcov = p.mu, p.cov
N = tf.shape(Xmu)[0] - 1
var_Z = kernel.variance * inducing_variable.Z # MxD
tiled_Z = tf.tile(tf.expand_dims(var_Z, 0), (N, 1, 1)) # NxMxD
eXX = Xcov[1, :-1] + (Xmu[:-1][..., None] * Xmu[1:][:, None, :]) # NxDxD
return tf.linalg.matmul(tiled_Z, eXX)
@dispatch.expectation.register(
(Gaussian, DiagonalGaussian), kernels.Linear, InducingPoints, kernels.Linear, InducingPoints
)
def _expectation_gaussian_linear_inducingpoints__linear_inducingpoints(
p: Union[Gaussian, DiagonalGaussian],
kern1: kernels.Linear,
feat1: InducingPoints,
kern2: kernels.Linear,
feat2: InducingPoints,
nghp: None = None,
) -> tf.Tensor:
"""
Compute the expectation:
expectation[n] = <Ka_{Z1, x_n} Kb_{x_n, Z2}>_p(x_n)
- Ka_{.,.}, Kb_{.,.} :: Linear kernels
Ka and Kb as well as Z1 and Z2 can differ from each other, but this is supported
only if the Gaussian p is Diagonal (p.cov NxD) and Ka, Kb have disjoint active_dims
in which case the joint expectations simplify into a product of expectations
:return: NxMxM
"""
if kern1.on_separate_dims(kern2) and isinstance(
p, DiagonalGaussian
): # no joint expectations required
eKxz1 = expectation(p, (kern1, feat1))
eKxz2 = expectation(p, (kern2, feat2))
return eKxz1[:, :, None] * eKxz2[:, None, :]
if kern1 != kern2 or feat1 != feat2:
raise NotImplementedError(
"The expectation over two kernels has only an "
"analytical implementation if both kernels are equal."
)
kernel = kern1
inducing_variable = feat1
# use only active dimensions
Xcov = kernel.slice_cov(tf.linalg.diag(p.cov) if isinstance(p, DiagonalGaussian) else p.cov)
Z, Xmu = kernel.slice(inducing_variable.Z, p.mu)
N = tf.shape(Xmu)[0]
var_Z = kernel.variance * Z
tiled_Z = tf.tile(tf.expand_dims(var_Z, 0), (N, 1, 1)) # NxMxD
XX = Xcov + tf.expand_dims(Xmu, 1) * tf.expand_dims(Xmu, 2) # NxDxD
return tf.linalg.matmul(tf.linalg.matmul(tiled_Z, XX), tiled_Z, transpose_b=True)
```

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