| 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 ( |
| broadcast_all, |
| clamp_probs, |
| lazy_property, |
| logits_to_probs, |
| probs_to_logits, |
| ) |
| from torch.nn.functional import binary_cross_entropy_with_logits |
| |
| __all__ = ["ContinuousBernoulli"] |
| |
| |
| 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) |
| |
| 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() |
| |
| 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) |
| |
| 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) |
| |
| 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() |
| ) |
| |
| 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), |
| ) |
| |
| 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, |
| ) |
| |
| 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) |
