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

mean_functions.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.
# noqa: F811
from typing import Type, Union
import tensorflow as tf
from .. import mean_functions as mfn
from ..probability_distributions import Gaussian
from . import dispatch
from .expectations import expectation
NoneType: Type[None] = type(None)
@dispatch.expectation.register(Gaussian, (mfn.Linear, mfn.Constant), NoneType, NoneType, NoneType)
def _expectation_gaussian_linear(
p: Gaussian,
mean: Union[mfn.Linear, mfn.Constant],
_: None,
__: None,
___: None,
nghp: None = None,
) -> tf.Tensor:
"""
Compute the expectation:
<m(X)>_p(X)
- m(x) :: Linear, Identity or Constant mean function
:return: NxQ
"""
return mean(p.mu)
@dispatch.expectation.register(Gaussian, mfn.Constant, NoneType, mfn.Constant, NoneType)
def _expectation_gaussian_constant__constant(
p: Gaussian, mean1: mfn.Constant, _: None, mean2: mfn.Constant, __: None, nghp: None = None
) -> tf.Tensor:
"""
Compute the expectation:
expectation[n] = <m1(x_n)^T m2(x_n)>_p(x_n)
- m1(.), m2(.) :: Constant mean functions
:return: NxQ1xQ2
"""
return mean1(p.mu)[:, :, None] * mean2(p.mu)[:, None, :]
@dispatch.expectation.register(Gaussian, mfn.Constant, NoneType, mfn.MeanFunction, NoneType)
def _expectation_gaussian_constant__meanfunction(
p: Gaussian, mean1: mfn.Constant, _: None, mean2: mfn.Constant, __: None, nghp: None = None
) -> tf.Tensor:
"""
Compute the expectation:
expectation[n] = <m1(x_n)^T m2(x_n)>_p(x_n)
- m1(.) :: Constant mean function
- m2(.) :: General mean function
:return: NxQ1xQ2
"""
e_mean2 = expectation(p, mean2)
return mean1(p.mu)[:, :, None] * e_mean2[:, None, :]
@dispatch.expectation.register(Gaussian, mfn.MeanFunction, NoneType, mfn.Constant, NoneType)
def _expectation_gaussian_meanfunction__constant(
p: Gaussian,
mean1: mfn.MeanFunction,
_: None,
mean2: mfn.MeanFunction,
__: None,
nghp: None = None,
) -> tf.Tensor:
"""
Compute the expectation:
expectation[n] = <m1(x_n)^T m2(x_n)>_p(x_n)
- m1(.) :: General mean function
- m2(.) :: Constant mean function
:return: NxQ1xQ2
"""
e_mean1 = expectation(p, mean1)
return e_mean1[:, :, None] * mean2(p.mu)[:, None, :]
@dispatch.expectation.register(Gaussian, mfn.Identity, NoneType, mfn.Identity, NoneType)
def _expectation_gaussian_identity__identity(
p: Gaussian, mean1: mfn.Identity, _: None, mean2: mfn.Identity, __: None, nghp: None = None
) -> tf.Tensor:
"""
Compute the expectation:
expectation[n] = <m1(x_n)^T m2(x_n)>_p(x_n)
- m1(.), m2(.) :: Identity mean functions
:return: NxDxD
"""
return p.cov + (p.mu[:, :, None] * p.mu[:, None, :])
@dispatch.expectation.register(Gaussian, mfn.Identity, NoneType, mfn.Linear, NoneType)
def _expectation_gaussian_identity__linear(
p: Gaussian, mean1: mfn.Identity, _: None, mean2: mfn.Linear, __: None, nghp: None = None
) -> tf.Tensor:
"""
Compute the expectation:
expectation[n] = <m1(x_n)^T m2(x_n)>_p(x_n)
- m1(.) :: Identity mean function
- m2(.) :: Linear mean function
:return: NxDxQ
"""
N = tf.shape(p.mu)[0]
e_xxt = p.cov + (p.mu[:, :, None] * p.mu[:, None, :]) # NxDxD
e_xxt_A = tf.linalg.matmul(e_xxt, tf.tile(mean2.A[None, ...], (N, 1, 1))) # NxDxQ
e_x_bt = p.mu[:, :, None] * mean2.b[None, None, :] # NxDxQ
return e_xxt_A + e_x_bt
@dispatch.expectation.register(Gaussian, mfn.Linear, NoneType, mfn.Identity, NoneType)
def _expectation_gaussian_linear__identity(
p: Gaussian, mean1: mfn.Linear, _: None, mean2: mfn.Identity, __: None, nghp: None = None
) -> tf.Tensor:
"""
Compute the expectation:
expectation[n] = <m1(x_n)^T m2(x_n)>_p(x_n)
- m1(.) :: Linear mean function
- m2(.) :: Identity mean function
:return: NxQxD
"""
N = tf.shape(p.mu)[0]
e_xxt = p.cov + (p.mu[:, :, None] * p.mu[:, None, :]) # NxDxD
e_A_xxt = tf.linalg.matmul(
tf.tile(mean1.A[None, ...], (N, 1, 1)), e_xxt, transpose_a=True
) # NxQxD
e_b_xt = mean1.b[None, :, None] * p.mu[:, None, :] # NxQxD
return e_A_xxt + e_b_xt
@dispatch.expectation.register(Gaussian, mfn.Linear, NoneType, mfn.Linear, NoneType)
def _expectation_gaussian_linear__linear(
p: Gaussian, mean1: mfn.Linear, _: None, mean2: mfn.Linear, __: None, nghp: None = None
) -> tf.Tensor:
"""
Compute the expectation:
expectation[n] = <m1(x_n)^T m2(x_n)>_p(x_n)
- m1(.), m2(.) :: Linear mean functions
:return: NxQ1xQ2
"""
e_xxt = p.cov + (p.mu[:, :, None] * p.mu[:, None, :]) # NxDxD
e_A1t_xxt_A2 = tf.einsum("iq,nij,jz->nqz", mean1.A, e_xxt, mean2.A) # NxQ1xQ2
e_A1t_x_b2t = tf.einsum("iq,ni,z->nqz", mean1.A, p.mu, mean2.b) # NxQ1xQ2
e_b1_xt_A2 = tf.einsum("q,ni,iz->nqz", mean1.b, p.mu, mean2.A) # NxQ1xQ2
e_b1_b2t = mean1.b[:, None] * mean2.b[None, :] # Q1xQ2
return e_A1t_xxt_A2 + e_A1t_x_b2t + e_b1_xt_A2 + e_b1_b2t
```

Computing file changes ...