Source code for gpflow.expectations.expectations

# Copyright 2018 The GPflow Contributors. All Rights Reserved.
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# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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# http://www.apache.org/licenses/LICENSE-2.0
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# Unless required by applicable law or agreed to in writing, software
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from typing import Optional, Tuple, Union, cast

import tensorflow as tf

from ..base import TensorType
from ..inducing_variables import InducingVariables
from ..kernels import Kernel
from ..mean_functions import MeanFunction
from ..probability_distributions import (
    DiagonalGaussian,
    Gaussian,
    MarkovGaussian,
    ProbabilityDistribution,
)
from . import dispatch

ProbabilityDistributionLike = Union[ProbabilityDistribution, Tuple[TensorType, TensorType]]
"""
Either a prabability distribution, or a tuple of mean, covariance that is turned into an
appropriate Gaussian distribution, depending on the shape of the covariance.
"""

ExpectationObject = Union[Kernel, MeanFunction, None]
PackedExpectationObject = Union[ExpectationObject, Tuple[Kernel, InducingVariables]]


[docs]def expectation( p: ProbabilityDistributionLike, obj1: PackedExpectationObject, obj2: PackedExpectationObject = None, nghp: Optional[int] = None, ) -> tf.Tensor: """ Compute the expectation <obj1(x) obj2(x)>_p(x) Uses multiple-dispatch to select an analytical implementation, if one is available. If not, it falls back to quadrature. :type p: (mu, cov) tuple or a `ProbabilityDistribution` object :type obj1: kernel, mean function, (kernel, inducing_variable), or None :type obj2: kernel, mean function, (kernel, inducing_variable), or None :param int nghp: passed to `_quadrature_expectation` to set the number of Gauss-Hermite points used: `num_gauss_hermite_points` :return: a 1-D, 2-D, or 3-D tensor containing the expectation Allowed combinations - Psi statistics: >>> eKdiag = expectation(p, kernel) (N) # Psi0 >>> eKxz = expectation(p, (kernel, inducing_variable)) (NxM) # Psi1 >>> exKxz = expectation(p, identity_mean, (kernel, inducing_variable)) (NxDxM) >>> eKzxKxz = expectation(p, (kernel, inducing_variable), (kernel, inducing_variable)) (NxMxM) # Psi2 - kernels and mean functions: >>> eKzxMx = expectation(p, (kernel, inducing_variable), mean) (NxMxQ) >>> eMxKxz = expectation(p, mean, (kernel, inducing_variable)) (NxQxM) - only mean functions: >>> eMx = expectation(p, mean) (NxQ) >>> eM1x_M2x = expectation(p, mean1, mean2) (NxQ1xQ2) .. note:: mean(x) is 1xQ (row vector) - different kernels. This occurs, for instance, when we are calculating Psi2 for Sum kernels: >>> eK1zxK2xz = expectation(p, (kern1, inducing_variable), (kern2, inducing_variable)) (NxMxM) """ p, obj1, feat1, obj2, feat2 = _init_expectation(p, obj1, obj2) try: return dispatch.expectation(p, obj1, feat1, obj2, feat2, nghp=nghp) except NotImplementedError as error: return dispatch.quadrature_expectation(p, obj1, feat1, obj2, feat2, nghp=nghp)
[docs]def quadrature_expectation( p: ProbabilityDistributionLike, obj1: PackedExpectationObject, obj2: PackedExpectationObject = None, nghp: Optional[int] = None, ) -> tf.Tensor: """ Compute the expectation <obj1(x) obj2(x)>_p(x) Uses Gauss-Hermite quadrature for approximate integration. :type p: (mu, cov) tuple or a `ProbabilityDistribution` object :type obj1: kernel, mean function, (kernel, inducing_variable), or None :type obj2: kernel, mean function, (kernel, inducing_variable), or None :param int num_gauss_hermite_points: passed to `_quadrature_expectation` to set the number of Gauss-Hermite points used :return: a 1-D, 2-D, or 3-D tensor containing the expectation """ print(f"2. p={p}, obj1={obj1}, obj2={obj2}") p, obj1, feat1, obj2, feat2 = _init_expectation(p, obj1, obj2) return dispatch.quadrature_expectation(p, obj1, feat1, obj2, feat2, nghp=nghp)
def _init_expectation( p: ProbabilityDistributionLike, obj1: PackedExpectationObject, obj2: PackedExpectationObject ) -> Tuple[ ProbabilityDistribution, ExpectationObject, Optional[InducingVariables], ExpectationObject, Optional[InducingVariables], ]: if isinstance(p, tuple): mu, cov = p classes = [DiagonalGaussian, Gaussian, MarkovGaussian] p = classes[cov.ndim - 2](*p) obj1, feat1 = obj1 if isinstance(obj1, tuple) else (obj1, None) obj2, feat2 = obj2 if isinstance(obj2, tuple) else (obj2, None) return ( cast(ProbabilityDistribution, p), cast(ExpectationObject, obj1), cast(Optional[InducingVariables], feat1), cast(ExpectationObject, obj2), cast(Optional[InducingVariables], feat2), )