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import torch |
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from torch import nan, Tensor |
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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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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) -> Tensor: |
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return _moments(self.concentration1, self.concentration0, 1) |
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@property |
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def mode(self) -> Tensor: |
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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) -> Tensor: |
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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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