Source code for gpytorch.utils.quadrature

#!/usr/bin/env python3

import math

import numpy as np
import torch
from torch.nn import Module

from .. import settings

def _pad_with_singletons(obj: torch.Tensor, num_singletons_before: int = 0, num_singletons_after: int = 0):
    Pad obj with singleton dimensions on the left and right

        >>> x = torch.randn(10, 5)
        >>> _pad_width_singletons(x, 2, 3).shape
        >>> # [1, 1, 10, 5, 1, 1, 1]
    new_shape = [1] * num_singletons_before + list(obj.shape) + [1] * num_singletons_after
    return obj.view(*new_shape)

[docs]class GaussHermiteQuadrature1D(Module): """ Implements Gauss-Hermite quadrature for integrating a function with respect to several 1D Gaussian distributions in batch mode. Within GPyTorch, this is useful primarily for computing expected log likelihoods for variational inference. This is implemented as a Module because Gauss-Hermite quadrature has a set of locations and weights that it should initialize one time, but that should obey parent calls to .cuda(), .double() etc. """ def __init__(self, num_locs=None): super().__init__() if num_locs is None: num_locs = settings.num_gauss_hermite_locs.value() self.num_locs = num_locs locations, weights = self._locs_and_weights(num_locs) self.locations = locations self.weights = weights def _apply(self, fn): self.locations = fn(self.locations) self.weights = fn(self.weights) return super(GaussHermiteQuadrature1D, self)._apply(fn) def _locs_and_weights(self, num_locs): """ Get locations and weights for Gauss-Hermite quadrature. Note that this is **not** intended to be used externally, because it directly creates tensors with no knowledge of a device or dtype to cast to. Instead, create a GaussHermiteQuadrature1D object and get the locations and weights from buffers. """ locations, weights = np.polynomial.hermite.hermgauss(num_locs) locations = torch.Tensor(locations) weights = torch.Tensor(weights) return locations, weights
[docs] def forward(self, func, gaussian_dists): """ Runs Gauss-Hermite quadrature on the callable func, integrating against the Gaussian distributions specified by gaussian_dists. Args: - func (callable): Function to integrate - gaussian_dists (Distribution): Either a MultivariateNormal whose covariance is assumed to be diagonal or a :obj:`torch.distributions.Normal`. Returns: - Result of integrating func against each univariate Gaussian in gaussian_dists. """ means = gaussian_dists.mean variances = gaussian_dists.variance locations = _pad_with_singletons(self.locations, num_singletons_before=0, num_singletons_after=means.dim()) shifted_locs = torch.sqrt(2.0 * variances) * locations + means log_probs = func(shifted_locs) weights = _pad_with_singletons(self.weights, num_singletons_before=0, num_singletons_after=log_probs.dim() - 1) res = (1 / math.sqrt(math.pi)) * (log_probs * weights) res = res.sum(tuple(range(self.locations.dim()))) return res