84 lines
3.0 KiB
Python
84 lines
3.0 KiB
Python
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import torch
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from torch.distributions import constraints
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from torch.distributions.exponential import Exponential
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from torch.distributions.gumbel import euler_constant
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from torch.distributions.transformed_distribution import TransformedDistribution
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from torch.distributions.transforms import AffineTransform, PowerTransform
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from torch.distributions.utils import broadcast_all
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__all__ = ["Weibull"]
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class Weibull(TransformedDistribution):
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r"""
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Samples from a two-parameter Weibull distribution.
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Example:
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>>> # xdoctest: +IGNORE_WANT("non-deterministic")
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>>> m = Weibull(torch.tensor([1.0]), torch.tensor([1.0]))
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>>> m.sample() # sample from a Weibull distribution with scale=1, concentration=1
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tensor([ 0.4784])
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Args:
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scale (float or Tensor): Scale parameter of distribution (lambda).
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concentration (float or Tensor): Concentration parameter of distribution (k/shape).
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"""
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arg_constraints = {
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"scale": constraints.positive,
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"concentration": constraints.positive,
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}
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support = constraints.positive
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def __init__(self, scale, concentration, validate_args=None):
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self.scale, self.concentration = broadcast_all(scale, concentration)
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self.concentration_reciprocal = self.concentration.reciprocal()
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base_dist = Exponential(
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torch.ones_like(self.scale), validate_args=validate_args
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)
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transforms = [
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PowerTransform(exponent=self.concentration_reciprocal),
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AffineTransform(loc=0, scale=self.scale),
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]
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super().__init__(base_dist, transforms, validate_args=validate_args)
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def expand(self, batch_shape, _instance=None):
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new = self._get_checked_instance(Weibull, _instance)
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new.scale = self.scale.expand(batch_shape)
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new.concentration = self.concentration.expand(batch_shape)
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new.concentration_reciprocal = new.concentration.reciprocal()
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base_dist = self.base_dist.expand(batch_shape)
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transforms = [
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PowerTransform(exponent=new.concentration_reciprocal),
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AffineTransform(loc=0, scale=new.scale),
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]
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super(Weibull, new).__init__(base_dist, transforms, validate_args=False)
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new._validate_args = self._validate_args
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return new
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@property
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def mean(self):
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return self.scale * torch.exp(torch.lgamma(1 + self.concentration_reciprocal))
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@property
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def mode(self):
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return (
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self.scale
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* ((self.concentration - 1) / self.concentration)
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** self.concentration.reciprocal()
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)
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@property
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def variance(self):
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return self.scale.pow(2) * (
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torch.exp(torch.lgamma(1 + 2 * self.concentration_reciprocal))
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- torch.exp(2 * torch.lgamma(1 + self.concentration_reciprocal))
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)
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def entropy(self):
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return (
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euler_constant * (1 - self.concentration_reciprocal)
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+ torch.log(self.scale * self.concentration_reciprocal)
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+ 1
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)
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