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# Source code for torch.distributions.continuous_bernoulli

from numbers import Number
import math

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

[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::

>>> 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)
# 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(getattr(self, 'probs')).all():
raise ValueError("The parameter {} has invalid values".format('probs'))
self.probs = clamp_probs(self.probs)
else:
is_scalar = isinstance(logits, Number)
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(ContinuousBernoulli, self).__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):
torch.gt(self.probs, self._lims[1]))

def _cut_probs(self):
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

@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

@property
def stddev(self):

@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. / 945.0 * x) * x

@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)
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)
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)
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()
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


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