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import math |
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import torch |
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from torch import inf, Tensor |
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from torch.distributions import constraints |
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from torch.distributions.cauchy import Cauchy |
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from torch.distributions.transformed_distribution import TransformedDistribution |
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from torch.distributions.transforms import AbsTransform |
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__all__ = ["HalfCauchy"] |
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class HalfCauchy(TransformedDistribution): |
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r""" |
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Creates a half-Cauchy distribution parameterized by `scale` where:: |
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X ~ Cauchy(0, scale) |
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Y = |X| ~ HalfCauchy(scale) |
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Example:: |
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>>> # xdoctest: +IGNORE_WANT("non-deterministic") |
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>>> m = HalfCauchy(torch.tensor([1.0])) |
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>>> m.sample() # half-cauchy distributed with scale=1 |
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tensor([ 2.3214]) |
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Args: |
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scale (float or Tensor): scale of the full Cauchy distribution |
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""" |
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arg_constraints = {"scale": constraints.positive} |
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support = constraints.nonnegative |
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has_rsample = True |
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def __init__(self, scale, validate_args=None): |
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base_dist = Cauchy(0, scale, validate_args=False) |
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super().__init__(base_dist, AbsTransform(), validate_args=validate_args) |
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def expand(self, batch_shape, _instance=None): |
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new = self._get_checked_instance(HalfCauchy, _instance) |
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return super().expand(batch_shape, _instance=new) |
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@property |
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def scale(self) -> Tensor: |
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return self.base_dist.scale |
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@property |
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def mean(self) -> Tensor: |
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return torch.full( |
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self._extended_shape(), |
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math.inf, |
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dtype=self.scale.dtype, |
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device=self.scale.device, |
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) |
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@property |
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def mode(self) -> Tensor: |
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return torch.zeros_like(self.scale) |
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@property |
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def variance(self) -> Tensor: |
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return self.base_dist.variance |
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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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value = torch.as_tensor( |
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value, dtype=self.base_dist.scale.dtype, device=self.base_dist.scale.device |
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) |
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log_prob = self.base_dist.log_prob(value) + math.log(2) |
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log_prob = torch.where(value >= 0, log_prob, -inf) |
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return log_prob |
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def cdf(self, value): |
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if self._validate_args: |
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self._validate_sample(value) |
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return 2 * self.base_dist.cdf(value) - 1 |
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def icdf(self, prob): |
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return self.base_dist.icdf((prob + 1) / 2) |
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def entropy(self): |
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return self.base_dist.entropy() - math.log(2) |
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