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

misc.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 Optional, Type, Union, cast
import tensorflow as tf
from .. import kernels
from .. import mean_functions as mfn
from ..inducing_variables import InducingPoints, InducingVariables
from ..probability_distributions import DiagonalGaussian, Gaussian, MarkovGaussian
from . import dispatch
from .expectations import ExpectationObject, PackedExpectationObject, expectation
NoneType: Type[None] = type(None)
# ================ exKxz transpose and mean function handling =================
@dispatch.expectation.register(
(Gaussian, MarkovGaussian), mfn.Identity, NoneType, kernels.Linear, InducingPoints
)
def _expectation_gaussian__linear_inducingpoints(
p: Union[Gaussian, MarkovGaussian],
mean: mfn.Identity,
_: None,
kernel: kernels.Linear,
inducing_variable: InducingPoints,
nghp: None = None,
) -> tf.Tensor:
"""
Compute the expectation:
expectation[n] = <x_n K_{x_n, Z}>_p(x_n)
- K_{.,} :: Linear kernel
or the equivalent for MarkovGaussian
:return: NxDxM
"""
return tf.linalg.adjoint(expectation(p, (kernel, inducing_variable), mean))
@dispatch.expectation.register(
(Gaussian, MarkovGaussian), kernels.Kernel, InducingVariables, mfn.MeanFunction, NoneType
)
def _expectation_gaussian_kernel_inducingvariables__meanfunction(
p: Union[Gaussian, MarkovGaussian],
kernel: kernels.Kernel,
inducing_variable: InducingVariables,
mean: mfn.MeanFunction,
_: None,
nghp: None = None,
) -> tf.Tensor:
"""
Compute the expectation:
expectation[n] = <K_{Z, x_n} m(x_n)>_p(x_n)
or the equivalent for MarkovGaussian
:return: NxMxQ
"""
return tf.linalg.adjoint(expectation(p, mean, (kernel, inducing_variable), nghp=nghp))
@dispatch.expectation.register(Gaussian, mfn.Constant, NoneType, kernels.Kernel, InducingPoints)
def _expectation_gaussian_constant__kernel_inducingpoints(
p: Gaussian,
constant_mean: mfn.Constant,
_: None,
kernel: kernels.Kernel,
inducing_variable: InducingPoints,
nghp: None = None,
) -> tf.Tensor:
"""
Compute the expectation:
expectation[n] = <m(x_n)^T K_{x_n, Z}>_p(x_n)
- m(x_i) = c :: Constant function
- K_{.,.} :: Kernel function
:return: NxQxM
"""
c = constant_mean(p.mu) # NxQ
eKxz = expectation(p, (kernel, inducing_variable), nghp=nghp) # NxM
return c[..., None] * eKxz[:, None, :]
@dispatch.expectation.register(Gaussian, mfn.Linear, NoneType, kernels.Kernel, InducingPoints)
def _expectation_gaussian_linear__kernel_inducingpoints(
p: Gaussian,
linear_mean: mfn.Linear,
_: None,
kernel: kernels.Kernel,
inducing_variable: InducingPoints,
nghp: None = None,
) -> tf.Tensor:
"""
Compute the expectation:
expectation[n] = <m(x_n)^T K_{x_n, Z}>_p(x_n)
- m(x_i) = A x_i + b :: Linear mean function
- K_{.,.} :: Kernel function
:return: NxQxM
"""
N = tf.shape(p.mu)[0]
D = tf.shape(p.mu)[1]
exKxz = expectation(p, mfn.Identity(D), (kernel, inducing_variable), nghp=nghp)
eKxz = expectation(p, (kernel, inducing_variable), nghp=nghp)
eAxKxz = tf.linalg.matmul(
tf.tile(linear_mean.A[None, :, :], (N, 1, 1)), exKxz, transpose_a=True
)
ebKxz = linear_mean.b[None, :, None] * eKxz[:, None, :]
return eAxKxz + ebKxz
@dispatch.expectation.register(Gaussian, mfn.Identity, NoneType, kernels.Kernel, InducingPoints)
def _expectation_gaussian__kernel_inducingpoints(
p: Gaussian,
identity_mean: mfn.Identity,
_: None,
kernel: kernels.Kernel,
inducing_variable: InducingPoints,
nghp: None = None,
) -> tf.Tensor:
"""
This prevents infinite recursion for kernels that don't have specific
implementations of _expectation(p, identity_mean, None, kernel, inducing_variable).
Recursion can arise because Identity is a subclass of Linear mean function
so _expectation(p, linear_mean, none, kernel, inducing_variable) would call itself.
More specific signatures (e.g. (p, identity_mean, None, RBF, inducing_variable)) will
be found and used whenever available
"""
raise NotImplementedError
# ============== Conversion to Gaussian from Diagonal or Markov ===============
# Catching missing DiagonalGaussian implementations by converting to full Gaussian:
@dispatch.expectation.register(
DiagonalGaussian, object, (InducingVariables, NoneType), object, (InducingVariables, NoneType)
)
def _expectation_diagonal_generic(
p: DiagonalGaussian,
obj1: ExpectationObject,
feat1: Optional[InducingVariables],
obj2: ExpectationObject,
feat2: Optional[InducingVariables],
nghp: None = None,
) -> tf.Tensor:
gaussian = Gaussian(p.mu, tf.linalg.diag(p.cov))
return expectation(
gaussian,
cast(PackedExpectationObject, (obj1, feat1)),
cast(PackedExpectationObject, (obj2, feat2)),
nghp=nghp,
)
# Catching missing MarkovGaussian implementations by converting to Gaussian (when indifferent):
@dispatch.expectation.register(
MarkovGaussian, object, (InducingVariables, NoneType), object, (InducingVariables, NoneType)
)
def _expectation_markov_generic(
p: MarkovGaussian,
obj1: ExpectationObject,
feat1: Optional[InducingVariables],
obj2: ExpectationObject,
feat2: Optional[InducingVariables],
nghp: None = None,
) -> tf.Tensor:
"""
Nota Bene: if only one object is passed, obj1 is
associated with x_n, whereas obj2 with x_{n+1}
"""
if obj2 is None:
gaussian = Gaussian(p.mu[:-1], p.cov[0, :-1])
return expectation(gaussian, cast(PackedExpectationObject, (obj1, feat1)), nghp=nghp)
elif obj1 is None:
gaussian = Gaussian(p.mu[1:], p.cov[0, 1:])
return expectation(gaussian, cast(PackedExpectationObject, (obj2, feat2)), nghp=nghp)
else:
return expectation(
p,
cast(PackedExpectationObject, (obj1, feat1)),
cast(PackedExpectationObject, (obj2, feat2)),
nghp=nghp,
)
```

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