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from numbers import Number |
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import math |
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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 broadcast_all, probs_to_logits, logits_to_probs, lazy_property, clamp_probs |
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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-deterinistic") |
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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, |
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'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__(self, probs=None, logits=None, lims=(0.499, 0.501), validate_args=None): |
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if (probs is None) == (logits is None): |
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raise ValueError("Either `probs` or `logits` must be specified, but not both.") |
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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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if validate_args is not None: |
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if not self.arg_constraints['probs'].check(getattr(self, 'probs')).all(): |
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raise ValueError("The parameter {} has invalid values".format('probs')) |
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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(ContinuousBernoulli, self).__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(torch.le(self.probs, self._lims[0]), |
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torch.gt(self.probs, self._lims[1])) |
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def _cut_probs(self): |
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return torch.where(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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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(torch.le(cut_probs, 0.5), |
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cut_probs, |
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torch.zeros_like(cut_probs)) |
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cut_probs_above_half = torch.where(torch.ge(cut_probs, 0.5), |
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cut_probs, |
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torch.ones_like(cut_probs)) |
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log_norm = torch.log(torch.abs(torch.log1p(-cut_probs) - torch.log(cut_probs))) - 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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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 / (torch.log1p(-cut_probs) - torch.log(cut_probs)) |
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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(1.0 - 2.0 * cut_probs, 2) + 1.0 / torch.pow( |
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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. / 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 -binary_cross_entropy_with_logits(logits, value, reduction='none') + self._cont_bern_log_norm() |
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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 = (torch.pow(cut_probs, value) * torch.pow(1.0 - cut_probs, 1.0 - value) |
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+ cut_probs - 1.0) / (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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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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(torch.log1p(-cut_probs + value * (2.0 * cut_probs - 1.0)) |
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- torch.log1p(-cut_probs)) / (torch.log(cut_probs) - torch.log1p(-cut_probs)), |
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value) |
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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 self.mean * (log_probs0 - log_probs1) - self._cont_bern_log_norm() - log_probs0 |
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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(torch.le(x, self._lims[0] - 0.5), |
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torch.gt(x, self._lims[1] - 0.5)) |
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cut_nat_params = torch.where(out_unst_reg, |
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x, |
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(self._lims[0] - 0.5) * torch.ones_like(x)) |
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log_norm = torch.log(torch.abs(torch.exp(cut_nat_params) - 1.0)) - torch.log(torch.abs(cut_nat_params)) |
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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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