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import math
from numbers import Number
import torch
from torch.distributions import constraints
from torch.distributions.transformed_distribution import TransformedDistribution
from torch.distributions.transforms import AffineTransform, ExpTransform
from torch.distributions.uniform import Uniform
from torch.distributions.utils import broadcast_all, euler_constant
__all__ = ["Gumbel"]
class Gumbel(TransformedDistribution):
r"""
Samples from a Gumbel Distribution.
Examples::
>>> # xdoctest: +IGNORE_WANT("non-deterministic")
>>> m = Gumbel(torch.tensor([1.0]), torch.tensor([2.0]))
>>> m.sample() # sample from Gumbel distribution with loc=1, scale=2
tensor([ 1.0124])
Args:
loc (float or Tensor): Location parameter of the distribution
scale (float or Tensor): Scale parameter of the distribution
"""
arg_constraints = {"loc": constraints.real, "scale": constraints.positive}
support = constraints.real
def __init__(self, loc, scale, validate_args=None):
self.loc, self.scale = broadcast_all(loc, scale)
finfo = torch.finfo(self.loc.dtype)
if isinstance(loc, Number) and isinstance(scale, Number):
base_dist = Uniform(finfo.tiny, 1 - finfo.eps, validate_args=validate_args)
else:
base_dist = Uniform(
torch.full_like(self.loc, finfo.tiny),
torch.full_like(self.loc, 1 - finfo.eps),
validate_args=validate_args,
)
transforms = [
ExpTransform().inv,
AffineTransform(loc=0, scale=-torch.ones_like(self.scale)),
ExpTransform().inv,
AffineTransform(loc=loc, scale=-self.scale),
]
super().__init__(base_dist, transforms, validate_args=validate_args)
def expand(self, batch_shape, _instance=None):
new = self._get_checked_instance(Gumbel, _instance)
new.loc = self.loc.expand(batch_shape)
new.scale = self.scale.expand(batch_shape)
return super().expand(batch_shape, _instance=new)
# Explicitly defining the log probability function for Gumbel due to precision issues
def log_prob(self, value):
if self._validate_args:
self._validate_sample(value)
y = (self.loc - value) / self.scale
return (y - y.exp()) - self.scale.log()
@property
def mean(self):
return self.loc + self.scale * euler_constant
@property
def mode(self):
return self.loc
@property
def stddev(self):
return (math.pi / math.sqrt(6)) * self.scale
@property
def variance(self):
return self.stddev.pow(2)
def entropy(self):
return self.scale.log() + (1 + euler_constant)
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