166 lines
5.8 KiB
Python
166 lines
5.8 KiB
Python
import torch
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from torch.distributions import constraints
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from torch.distributions.distribution import Distribution
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from torch.distributions.utils import (
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broadcast_all,
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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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__all__ = ["Binomial"]
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def _clamp_by_zero(x):
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# works like clamp(x, min=0) but has grad at 0 is 0.5
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return (x.clamp(min=0) + x - x.clamp(max=0)) / 2
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class Binomial(Distribution):
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r"""
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Creates a Binomial distribution parameterized by :attr:`total_count` and
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either :attr:`probs` or :attr:`logits` (but not both). :attr:`total_count` must be
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broadcastable with :attr:`probs`/:attr:`logits`.
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Example::
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>>> # xdoctest: +IGNORE_WANT("non-deterministic")
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>>> m = Binomial(100, torch.tensor([0 , .2, .8, 1]))
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>>> x = m.sample()
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tensor([ 0., 22., 71., 100.])
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>>> m = Binomial(torch.tensor([[5.], [10.]]), torch.tensor([0.5, 0.8]))
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>>> x = m.sample()
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tensor([[ 4., 5.],
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[ 7., 6.]])
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Args:
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total_count (int or Tensor): number of Bernoulli trials
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probs (Tensor): Event probabilities
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logits (Tensor): Event log-odds
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"""
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arg_constraints = {
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"total_count": constraints.nonnegative_integer,
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"probs": constraints.unit_interval,
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"logits": constraints.real,
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}
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has_enumerate_support = True
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def __init__(self, total_count=1, probs=None, logits=None, validate_args=None):
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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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(
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self.total_count,
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self.probs,
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) = broadcast_all(total_count, probs)
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self.total_count = self.total_count.type_as(self.probs)
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else:
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(
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self.total_count,
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self.logits,
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) = broadcast_all(total_count, logits)
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self.total_count = self.total_count.type_as(self.logits)
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self._param = self.probs if probs is not None else self.logits
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batch_shape = self._param.size()
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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(Binomial, _instance)
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batch_shape = torch.Size(batch_shape)
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new.total_count = self.total_count.expand(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(Binomial, 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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@constraints.dependent_property(is_discrete=True, event_dim=0)
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def support(self):
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return constraints.integer_interval(0, self.total_count)
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@property
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def mean(self):
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return self.total_count * self.probs
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@property
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def mode(self):
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return ((self.total_count + 1) * self.probs).floor().clamp(max=self.total_count)
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@property
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def variance(self):
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return self.total_count * self.probs * (1 - self.probs)
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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 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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with torch.no_grad():
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return torch.binomial(
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self.total_count.expand(shape), self.probs.expand(shape)
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)
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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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log_factorial_n = torch.lgamma(self.total_count + 1)
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log_factorial_k = torch.lgamma(value + 1)
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log_factorial_nmk = torch.lgamma(self.total_count - value + 1)
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# k * log(p) + (n - k) * log(1 - p) = k * (log(p) - log(1 - p)) + n * log(1 - p)
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# (case logit < 0) = k * logit - n * log1p(e^logit)
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# (case logit > 0) = k * logit - n * (log(p) - log(1 - p)) + n * log(p)
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# = k * logit - n * logit - n * log1p(e^-logit)
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# (merge two cases) = k * logit - n * max(logit, 0) - n * log1p(e^-|logit|)
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normalize_term = (
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self.total_count * _clamp_by_zero(self.logits)
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+ self.total_count * torch.log1p(torch.exp(-torch.abs(self.logits)))
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- log_factorial_n
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)
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return (
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value * self.logits - log_factorial_k - log_factorial_nmk - normalize_term
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)
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def entropy(self):
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total_count = int(self.total_count.max())
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if not self.total_count.min() == total_count:
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raise NotImplementedError(
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"Inhomogeneous total count not supported by `entropy`."
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)
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log_prob = self.log_prob(self.enumerate_support(False))
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return -(torch.exp(log_prob) * log_prob).sum(0)
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def enumerate_support(self, expand=True):
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total_count = int(self.total_count.max())
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if not self.total_count.min() == total_count:
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raise NotImplementedError(
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"Inhomogeneous total count not supported by `enumerate_support`."
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)
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values = torch.arange(
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1 + total_count, dtype=self._param.dtype, device=self._param.device
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)
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values = values.view((-1,) + (1,) * len(self._batch_shape))
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if expand:
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values = values.expand((-1,) + self._batch_shape)
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return values
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