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98 lines
3.4 KiB
98 lines
3.4 KiB
5 months ago
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import torch
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from torch import nan
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from torch.distributions import constraints
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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.uniform import Uniform
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from torch.distributions.utils import broadcast_all, euler_constant
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__all__ = ["Kumaraswamy"]
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def _moments(a, b, n):
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"""
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Computes nth moment of Kumaraswamy using using torch.lgamma
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"""
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arg1 = 1 + n / a
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log_value = torch.lgamma(arg1) + torch.lgamma(b) - torch.lgamma(arg1 + b)
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return b * torch.exp(log_value)
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class Kumaraswamy(TransformedDistribution):
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r"""
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Samples from a Kumaraswamy distribution.
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Example::
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>>> # xdoctest: +IGNORE_WANT("non-deterministic")
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>>> m = Kumaraswamy(torch.tensor([1.0]), torch.tensor([1.0]))
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>>> m.sample() # sample from a Kumaraswamy distribution with concentration alpha=1 and beta=1
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tensor([ 0.1729])
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Args:
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concentration1 (float or Tensor): 1st concentration parameter of the distribution
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(often referred to as alpha)
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concentration0 (float or Tensor): 2nd concentration parameter 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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"concentration1": constraints.positive,
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"concentration0": constraints.positive,
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}
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support = constraints.unit_interval
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has_rsample = True
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def __init__(self, concentration1, concentration0, validate_args=None):
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self.concentration1, self.concentration0 = broadcast_all(
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concentration1, concentration0
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)
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finfo = torch.finfo(self.concentration0.dtype)
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base_dist = Uniform(
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torch.full_like(self.concentration0, 0),
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torch.full_like(self.concentration0, 1),
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validate_args=validate_args,
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)
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transforms = [
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PowerTransform(exponent=self.concentration0.reciprocal()),
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AffineTransform(loc=1.0, scale=-1.0),
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PowerTransform(exponent=self.concentration1.reciprocal()),
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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(Kumaraswamy, _instance)
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new.concentration1 = self.concentration1.expand(batch_shape)
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new.concentration0 = self.concentration0.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):
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return _moments(self.concentration1, self.concentration0, 1)
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@property
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def mode(self):
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# Evaluate in log-space for numerical stability.
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log_mode = (
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self.concentration0.reciprocal() * (-self.concentration0).log1p()
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- (-self.concentration0 * self.concentration1).log1p()
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)
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log_mode[(self.concentration0 < 1) | (self.concentration1 < 1)] = nan
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return log_mode.exp()
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@property
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def variance(self):
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return _moments(self.concentration1, self.concentration0, 2) - torch.pow(
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self.mean, 2
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)
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def entropy(self):
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t1 = 1 - self.concentration1.reciprocal()
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t0 = 1 - self.concentration0.reciprocal()
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H0 = torch.digamma(self.concentration0 + 1) + euler_constant
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return (
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t0
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+ t1 * H0
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- torch.log(self.concentration1)
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- torch.log(self.concentration0)
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)
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