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import torch |
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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.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) -> Tensor: |
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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) -> Tensor: |
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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) -> Tensor: |
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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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