Source code for torch.distributions.exp_family

import torch
from torch.distributions.distribution import Distribution

__all__ = ["ExponentialFamily"]

[docs]class ExponentialFamily(Distribution): r""" ExponentialFamily is the abstract base class for probability distributions belonging to an exponential family, whose probability mass/density function has the form is defined below .. math:: p_{F}(x; \theta) = \exp(\langle t(x), \theta\rangle - F(\theta) + k(x)) where :math:`\theta` denotes the natural parameters, :math:`t(x)` denotes the sufficient statistic, :math:`F(\theta)` is the log normalizer function for a given family and :math:`k(x)` is the carrier measure. Note: This class is an intermediary between the `Distribution` class and distributions which belong to an exponential family mainly to check the correctness of the `.entropy()` and analytic KL divergence methods. We use this class to compute the entropy and KL divergence using the AD framework and Bregman divergences (courtesy of: Frank Nielsen and Richard Nock, Entropies and Cross-entropies of Exponential Families). """ @property def _natural_params(self): """ Abstract method for natural parameters. Returns a tuple of Tensors based on the distribution """ raise NotImplementedError def _log_normalizer(self, *natural_params): """ Abstract method for log normalizer function. Returns a log normalizer based on the distribution and input """ raise NotImplementedError @property def _mean_carrier_measure(self): """ Abstract method for expected carrier measure, which is required for computing entropy. """ raise NotImplementedError
[docs] def entropy(self): """ Method to compute the entropy using Bregman divergence of the log normalizer. """ result = -self._mean_carrier_measure nparams = [p.detach().requires_grad_() for p in self._natural_params] lg_normal = self._log_normalizer(*nparams) gradients = torch.autograd.grad(lg_normal.sum(), nparams, create_graph=True) result += lg_normal for np, g in zip(nparams, gradients): result -= (np * g).reshape(self._batch_shape + (-1,)).sum(-1) return result


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