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81 lines
2.4 KiB
81 lines
2.4 KiB
import torch
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from torch.distributions import constraints
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from torch.distributions.gamma import Gamma
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from torch.distributions.transformed_distribution import TransformedDistribution
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from torch.distributions.transforms import PowerTransform
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__all__ = ["InverseGamma"]
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class InverseGamma(TransformedDistribution):
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r"""
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Creates an inverse gamma distribution parameterized by :attr:`concentration` and :attr:`rate`
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where::
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X ~ Gamma(concentration, rate)
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Y = 1 / X ~ InverseGamma(concentration, rate)
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Example::
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>>> # xdoctest: +IGNORE_WANT("non-deterinistic")
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>>> m = InverseGamma(torch.tensor([2.0]), torch.tensor([3.0]))
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>>> m.sample()
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tensor([ 1.2953])
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Args:
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concentration (float or Tensor): shape parameter of the distribution
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(often referred to as alpha)
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rate (float or Tensor): rate = 1 / scale of the distribution
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(often referred to as beta)
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"""
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arg_constraints = {
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"concentration": constraints.positive,
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"rate": constraints.positive,
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}
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support = constraints.positive
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has_rsample = True
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def __init__(self, concentration, rate, validate_args=None):
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base_dist = Gamma(concentration, rate, validate_args=validate_args)
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neg_one = -base_dist.rate.new_ones(())
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super().__init__(
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base_dist, PowerTransform(neg_one), validate_args=validate_args
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)
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def expand(self, batch_shape, _instance=None):
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new = self._get_checked_instance(InverseGamma, _instance)
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return super().expand(batch_shape, _instance=new)
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@property
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def concentration(self):
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return self.base_dist.concentration
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@property
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def rate(self):
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return self.base_dist.rate
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@property
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def mean(self):
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result = self.rate / (self.concentration - 1)
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return torch.where(self.concentration > 1, result, torch.inf)
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@property
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def mode(self):
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return self.rate / (self.concentration + 1)
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@property
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def variance(self):
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result = self.rate.square() / (
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(self.concentration - 1).square() * (self.concentration - 2)
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)
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return torch.where(self.concentration > 2, result, torch.inf)
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def entropy(self):
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return (
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self.concentration
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+ self.rate.log()
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+ self.concentration.lgamma()
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- (1 + self.concentration) * self.concentration.digamma()
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)
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