Source code for gpflow.quadrature.base

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import abc
from typing import Any, Callable, Iterable, Tuple, Union

import tensorflow as tf

from ..base import TensorType


[docs]class GaussianQuadrature: """ Abstract class implementing quadrature methods to compute Gaussian Expectations. Inheriting classes must provide the method _build_X_W to create points and weights to be used for quadrature. """ @abc.abstractmethod def _build_X_W(self, mean: TensorType, var: TensorType) -> Tuple[tf.Tensor, tf.Tensor]: raise NotImplementedError def __call__( self, fun: Union[Callable[..., tf.Tensor], Iterable[Callable[..., tf.Tensor]]], mean: TensorType, var: TensorType, *args: Any, **kwargs: Any, ) -> tf.Tensor: r""" Compute the Gaussian Expectation of a function f: X ~ N(mean, var) E[f(X)] = ∫f(x, *args, **kwargs)p(x)dx Using the formula: E[f(X)] = sum_{i=1}^{N_quad_points} f(x_i) * w_i where x_i, w_i must be provided by the inheriting class through self._build_X_W. The computations broadcast along batch-dimensions, represented by [b1, b2, ..., bX]. :param fun: Callable or Iterable of Callables that operates elementwise, with signature f(X, *args, **kwargs). Moreover, it must satisfy the shape-mapping: X shape: [N_quad_points, b1, b2, ..., bX, d], usually [N_quad_points, N, d] f(X) shape: [N_quad_points, b1, b2, ...., bX, d'], usually [N_quad_points, N, 1] or [N_quad_points, N, d] In most cases, f should only operate over the last dimension of X :param mean: Array/Tensor with shape [b1, b2, ..., bX, d], usually [N, d], representing the mean of a d-Variate Gaussian distribution :param var: Array/Tensor with shape b1, b2, ..., bX, d], usually [N, d], representing the variance of a d-Variate Gaussian distribution :param *args: Passed to fun :param **kargs: Passed to fun :return: Array/Tensor with shape [b1, b2, ...., bX, d'], usually [N, d] or [N, 1] """ X, W = self._build_X_W(mean, var) if isinstance(fun, Iterable): return [tf.reduce_sum(f(X, *args, **kwargs) * W, axis=0) for f in fun] return tf.reduce_sum(fun(X, *args, **kwargs) * W, axis=0)
[docs] def logspace( self, fun: Union[Callable[..., tf.Tensor], Iterable[Callable[..., tf.Tensor]]], mean: TensorType, var: TensorType, *args: Any, **kwargs: Any, ) -> tf.Tensor: r""" Compute the Gaussian log-Expectation of a the exponential of a function f: X ~ N(mean, var) log E[exp[f(X)]] = log ∫exp[f(x, *args, **kwargs)]p(x)dx Using the formula: log E[exp[f(X)]] = log sum_{i=1}^{N_quad_points} exp[f(x_i) + log w_i] where x_i, w_i must be provided by the inheriting class through self._build_X_W. The computations broadcast along batch-dimensions, represented by [b1, b2, ..., bX]. :param fun: Callable or Iterable of Callables that operates elementwise, with signature f(X, *args, **kwargs). Moreover, it must satisfy the shape-mapping: X shape: [N_quad_points, b1, b2, ..., bX, d], usually [N_quad_points, N, d] f(X) shape: [N_quad_points, b1, b2, ...., bX, d'], usually [N_quad_points, N, 1] or [N_quad_points, N, d] In most cases, f should only operate over the last dimension of X :param mean: Array/Tensor with shape [b1, b2, ..., bX, d], usually [N, d], representing the mean of a d-Variate Gaussian distribution :param var: Array/Tensor with shape b1, b2, ..., bX, d], usually [N, d], representing the variance of a d-Variate Gaussian distribution :param *args: Passed to fun :param **kargs: Passed to fun :return: Array/Tensor with shape [b1, b2, ...., bX, d'], usually [N, d] or [N, 1] """ X, W = self._build_X_W(mean, var) logW = tf.math.log(W) if isinstance(fun, Iterable): return [tf.reduce_logsumexp(f(X, *args, **kwargs) + logW, axis=0) for f in fun] return tf.reduce_logsumexp(fun(X, *args, **kwargs) + logW, axis=0)