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from typing import Optional |
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from torch import Tensor |
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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.transformed_distribution import TransformedDistribution |
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from torch.distributions.transforms import AffineTransform, ExpTransform |
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from torch.distributions.utils import broadcast_all |
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from torch.types import _size |
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__all__ = ["Pareto"] |
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class Pareto(TransformedDistribution): |
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r""" |
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Samples from a Pareto Type 1 distribution. |
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Example:: |
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>>> # xdoctest: +IGNORE_WANT("non-deterministic") |
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>>> m = Pareto(torch.tensor([1.0]), torch.tensor([1.0])) |
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>>> m.sample() # sample from a Pareto distribution with scale=1 and alpha=1 |
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tensor([ 1.5623]) |
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Args: |
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scale (float or Tensor): Scale parameter of the distribution |
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alpha (float or Tensor): Shape parameter of the distribution |
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""" |
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arg_constraints = {"alpha": constraints.positive, "scale": constraints.positive} |
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def __init__( |
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self, scale: Tensor, alpha: Tensor, validate_args: Optional[bool] = None |
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) -> None: |
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self.scale, self.alpha = broadcast_all(scale, alpha) |
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base_dist = Exponential(self.alpha, validate_args=validate_args) |
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transforms = [ExpTransform(), AffineTransform(loc=0, scale=self.scale)] |
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super().__init__(base_dist, transforms, validate_args=validate_args) |
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def expand( |
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self, batch_shape: _size, _instance: Optional["Pareto"] = None |
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) -> "Pareto": |
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new = self._get_checked_instance(Pareto, _instance) |
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new.scale = self.scale.expand(batch_shape) |
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new.alpha = self.alpha.expand(batch_shape) |
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return super().expand(batch_shape, _instance=new) |
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@property |
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def mean(self) -> Tensor: |
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a = self.alpha.clamp(min=1) |
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return a * self.scale / (a - 1) |
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@property |
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def mode(self) -> Tensor: |
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return self.scale |
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@property |
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def variance(self) -> Tensor: |
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a = self.alpha.clamp(min=2) |
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return self.scale.pow(2) * a / ((a - 1).pow(2) * (a - 2)) |
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@constraints.dependent_property(is_discrete=False, event_dim=0) |
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def support(self) -> constraints.Constraint: |
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return constraints.greater_than_eq(self.scale) |
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def entropy(self) -> Tensor: |
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return (self.scale / self.alpha).log() + (1 + self.alpha.reciprocal()) |
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