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