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# Source code for torch.distributions.continuous_bernoulli

# mypy: allow-untyped-defs
import math
from numbers import Number

import torch
from torch.distributions import constraints
from torch.distributions.exp_family import ExponentialFamily
from torch.distributions.utils import (
clamp_probs,
lazy_property,
logits_to_probs,
probs_to_logits,
)
from torch.nn.functional import binary_cross_entropy_with_logits

__all__ = ["ContinuousBernoulli"]

[docs]class ContinuousBernoulli(ExponentialFamily): r""" Creates a continuous Bernoulli distribution parameterized by :attr:probs or :attr:logits (but not both). The distribution is supported in [0, 1] and parameterized by 'probs' (in (0,1)) or 'logits' (real-valued). Note that, unlike the Bernoulli, 'probs' does not correspond to a probability and 'logits' does not correspond to log-odds, but the same names are used due to the similarity with the Bernoulli. See [1] for more details. Example:: >>> # xdoctest: +IGNORE_WANT("non-deterministic") >>> m = ContinuousBernoulli(torch.tensor([0.3])) >>> m.sample() tensor([ 0.2538]) Args: probs (Number, Tensor): (0,1) valued parameters logits (Number, Tensor): real valued parameters whose sigmoid matches 'probs' [1] The continuous Bernoulli: fixing a pervasive error in variational autoencoders, Loaiza-Ganem G and Cunningham JP, NeurIPS 2019. https://arxiv.org/abs/1907.06845 """ arg_constraints = {"probs": constraints.unit_interval, "logits": constraints.real} support = constraints.unit_interval _mean_carrier_measure = 0 has_rsample = True def __init__( self, probs=None, logits=None, lims=(0.499, 0.501), validate_args=None ): if (probs is None) == (logits is None): raise ValueError( "Either probs or logits must be specified, but not both." ) if probs is not None: is_scalar = isinstance(probs, Number) (self.probs,) = broadcast_all(probs) # validate 'probs' here if necessary as it is later clamped for numerical stability # close to 0 and 1, later on; otherwise the clamped 'probs' would always pass if validate_args is not None: if not self.arg_constraints["probs"].check(self.probs).all(): raise ValueError("The parameter probs has invalid values") self.probs = clamp_probs(self.probs) else: is_scalar = isinstance(logits, Number) (self.logits,) = broadcast_all(logits) self._param = self.probs if probs is not None else self.logits if is_scalar: batch_shape = torch.Size() else: batch_shape = self._param.size() self._lims = lims super().__init__(batch_shape, validate_args=validate_args)
[docs] def expand(self, batch_shape, _instance=None): new = self._get_checked_instance(ContinuousBernoulli, _instance) new._lims = self._lims batch_shape = torch.Size(batch_shape) if "probs" in self.__dict__: new.probs = self.probs.expand(batch_shape) new._param = new.probs if "logits" in self.__dict__: new.logits = self.logits.expand(batch_shape) new._param = new.logits super(ContinuousBernoulli, new).__init__(batch_shape, validate_args=False) new._validate_args = self._validate_args return new
def _new(self, *args, **kwargs): return self._param.new(*args, **kwargs) def _outside_unstable_region(self): return torch.max( torch.le(self.probs, self._lims[0]), torch.gt(self.probs, self._lims[1]) ) def _cut_probs(self): return torch.where( self._outside_unstable_region(), self.probs, self._lims[0] * torch.ones_like(self.probs), ) def _cont_bern_log_norm(self): """computes the log normalizing constant as a function of the 'probs' parameter""" cut_probs = self._cut_probs() cut_probs_below_half = torch.where( torch.le(cut_probs, 0.5), cut_probs, torch.zeros_like(cut_probs) ) cut_probs_above_half = torch.where( torch.ge(cut_probs, 0.5), cut_probs, torch.ones_like(cut_probs) ) log_norm = torch.log( torch.abs(torch.log1p(-cut_probs) - torch.log(cut_probs)) ) - torch.where( torch.le(cut_probs, 0.5), torch.log1p(-2.0 * cut_probs_below_half), torch.log(2.0 * cut_probs_above_half - 1.0), ) x = torch.pow(self.probs - 0.5, 2) taylor = math.log(2.0) + (4.0 / 3.0 + 104.0 / 45.0 * x) * x return torch.where(self._outside_unstable_region(), log_norm, taylor) @property def mean(self): cut_probs = self._cut_probs() mus = cut_probs / (2.0 * cut_probs - 1.0) + 1.0 / ( torch.log1p(-cut_probs) - torch.log(cut_probs) ) x = self.probs - 0.5 taylor = 0.5 + (1.0 / 3.0 + 16.0 / 45.0 * torch.pow(x, 2)) * x return torch.where(self._outside_unstable_region(), mus, taylor) @property def stddev(self): return torch.sqrt(self.variance) @property def variance(self): cut_probs = self._cut_probs() vars = cut_probs * (cut_probs - 1.0) / torch.pow( 1.0 - 2.0 * cut_probs, 2 ) + 1.0 / torch.pow(torch.log1p(-cut_probs) - torch.log(cut_probs), 2) x = torch.pow(self.probs - 0.5, 2) taylor = 1.0 / 12.0 - (1.0 / 15.0 - 128.0 / 945.0 * x) * x return torch.where(self._outside_unstable_region(), vars, taylor) @lazy_property def logits(self): return probs_to_logits(self.probs, is_binary=True) @lazy_property def probs(self): return clamp_probs(logits_to_probs(self.logits, is_binary=True)) @property def param_shape(self): return self._param.size()
[docs] def sample(self, sample_shape=torch.Size()): shape = self._extended_shape(sample_shape) u = torch.rand(shape, dtype=self.probs.dtype, device=self.probs.device) with torch.no_grad(): return self.icdf(u)
[docs] def rsample(self, sample_shape=torch.Size()): shape = self._extended_shape(sample_shape) u = torch.rand(shape, dtype=self.probs.dtype, device=self.probs.device) return self.icdf(u)
[docs] def log_prob(self, value): if self._validate_args: self._validate_sample(value) logits, value = broadcast_all(self.logits, value) return ( -binary_cross_entropy_with_logits(logits, value, reduction="none") + self._cont_bern_log_norm() )
[docs] def cdf(self, value): if self._validate_args: self._validate_sample(value) cut_probs = self._cut_probs() cdfs = ( torch.pow(cut_probs, value) * torch.pow(1.0 - cut_probs, 1.0 - value) + cut_probs - 1.0 ) / (2.0 * cut_probs - 1.0) unbounded_cdfs = torch.where(self._outside_unstable_region(), cdfs, value) return torch.where( torch.le(value, 0.0), torch.zeros_like(value), torch.where(torch.ge(value, 1.0), torch.ones_like(value), unbounded_cdfs), )
[docs] def icdf(self, value): cut_probs = self._cut_probs() return torch.where( self._outside_unstable_region(), ( torch.log1p(-cut_probs + value * (2.0 * cut_probs - 1.0)) - torch.log1p(-cut_probs) ) / (torch.log(cut_probs) - torch.log1p(-cut_probs)), value, )
[docs] def entropy(self): log_probs0 = torch.log1p(-self.probs) log_probs1 = torch.log(self.probs) return ( self.mean * (log_probs0 - log_probs1) - self._cont_bern_log_norm() - log_probs0 )
@property def _natural_params(self): return (self.logits,) def _log_normalizer(self, x): """computes the log normalizing constant as a function of the natural parameter""" out_unst_reg = torch.max( torch.le(x, self._lims[0] - 0.5), torch.gt(x, self._lims[1] - 0.5) ) cut_nat_params = torch.where( out_unst_reg, x, (self._lims[0] - 0.5) * torch.ones_like(x) ) log_norm = torch.log(torch.abs(torch.exp(cut_nat_params) - 1.0)) - torch.log( torch.abs(cut_nat_params) ) taylor = 0.5 * x + torch.pow(x, 2) / 24.0 - torch.pow(x, 4) / 2880.0 return torch.where(out_unst_reg, log_norm, taylor)

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