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 check_shapes import check_shapes

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 @check_shapes( "mean: [batch..., D]", "var: [batch..., D]", "return[0]: [N_quad_points, batch..., D]", "return[1]: [N_quad_points, broadcast batch..., 1]", ) def _build_X_W(self, mean: TensorType, var: TensorType) -> Tuple[tf.Tensor, tf.Tensor]: raise NotImplementedError @check_shapes( "mean: [in_batch..., D]", "var: [in_batch..., D]", "return: [n_funs..., out_batch..., broadcast D]", ) 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. :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, batch..., d]. f(X) shape: [N_quad_points, batch..., broadcast d]. In most cases, f should only operate over the last dimension of X :param mean: Array/Tensor representing the mean of a d-Variate Gaussian distribution :param var: Array/Tensor representing the variance of a d-Variate Gaussian distribution :param args: Passed to fun :param kargs: Passed to fun :return: Gaussian expectation of fun """ 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] @check_shapes( "mean: [in_batch..., D]", "var: [in_batch..., D]", "return: [n_fun..., out_batch..., broadcast D]", ) 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 [batch...]. :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, batch..., d]. f(X) shape: [N_quad_points, batch..., broadcast d]. In most cases, f should only operate over the last dimension of X :param mean: Array/Tensor representing the mean of a d-Variate Gaussian distribution :param var: Array/Tensor representing the variance of a d-Variate Gaussian distribution :param args: Passed to fun :param kwargs: Passed to fun :return: Gaussian log-expectation of the exponential of a function f """ 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)