Source code for gpytorch.likelihoods.bernoulli_likelihood

#!/usr/bin/env python3

import warnings
from typing import Any

import torch
from torch import Tensor
from torch.distributions import Bernoulli

from ..distributions import base_distributions, MultivariateNormal
from ..functions import log_normal_cdf
from .likelihood import _OneDimensionalLikelihood

[docs]class BernoulliLikelihood(_OneDimensionalLikelihood): r""" Implements the Bernoulli likelihood used for GP classification, using Probit regression (i.e., the latent function is warped to be in [0,1] using the standard Normal CDF :math:`\Phi(x)`). Given the identity :math:`\Phi(-x) = 1-\Phi(x)`, we can write the likelihood compactly as: .. math:: \begin{equation*} p(Y=y|f)=\Phi((2y - 1)f) \end{equation*} .. note:: BernoulliLikelihood has an analytic marginal distribution. .. note:: The labels should take values in {0, 1}. """ has_analytic_marginal: bool = True def __init__(self) -> None: return super().__init__() def forward(self, function_samples: Tensor, *args: Any, **kwargs: Any) -> Bernoulli: output_probs = base_distributions.Normal(0, 1).cdf(function_samples) return base_distributions.Bernoulli(probs=output_probs) def log_marginal( self, observations: Tensor, function_dist: MultivariateNormal, *args: Any, **kwargs: Any ) -> Tensor: marginal = self.marginal(function_dist, *args, **kwargs) return marginal.log_prob(observations)
[docs] def marginal(self, function_dist: MultivariateNormal, *args: Any, **kwargs: Any) -> Bernoulli: r""" :return: Analytic marginal :math:`p(\mathbf y)`. """ mean = function_dist.mean var = function_dist.variance link = mean.div(torch.sqrt(1 + var)) output_probs = base_distributions.Normal(0, 1).cdf(link) return base_distributions.Bernoulli(probs=output_probs)
def expected_log_prob( self, observations: Tensor, function_dist: MultivariateNormal, *params: Any, **kwargs: Any ) -> Tensor: if torch.any(observations.eq(-1)): # Remove after 1.0 warnings.warn( "BernoulliLikelihood.expected_log_prob expects observations with labels in {0, 1}. " "Observations with labels in {-1, 1} are deprecated.", DeprecationWarning, ) else: observations = observations.mul(2).sub(1) # Custom function here so we can use log_normal_cdf rather than Normal.cdf # This is going to be less prone to overflow errors log_prob_lambda = lambda function_samples: log_normal_cdf(function_samples.mul(observations)) log_prob = self.quadrature(log_prob_lambda, function_dist) return log_prob