83 lines
3.0 KiB
Python
83 lines
3.0 KiB
Python
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from numbers import Number
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import torch
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from torch.distributions import constraints
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from torch.distributions.exp_family import ExponentialFamily
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from torch.distributions.utils import broadcast_all
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def _standard_gamma(concentration):
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return torch._standard_gamma(concentration)
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class Gamma(ExponentialFamily):
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r"""
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Creates a Gamma distribution parameterized by shape :attr:`concentration` and :attr:`rate`.
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Example::
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>>> m = Gamma(torch.tensor([1.0]), torch.tensor([1.0]))
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>>> m.sample() # Gamma distributed with concentration=1 and rate=1
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tensor([ 0.1046])
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Args:
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concentration (float or Tensor): shape parameter of the distribution
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(often referred to as alpha)
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rate (float or Tensor): rate = 1 / scale of the distribution
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(often referred to as beta)
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"""
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arg_constraints = {'concentration': constraints.positive, 'rate': constraints.positive}
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support = constraints.positive
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has_rsample = True
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_mean_carrier_measure = 0
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@property
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def mean(self):
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return self.concentration / self.rate
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@property
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def variance(self):
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return self.concentration / self.rate.pow(2)
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def __init__(self, concentration, rate, validate_args=None):
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self.concentration, self.rate = broadcast_all(concentration, rate)
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if isinstance(concentration, Number) and isinstance(rate, Number):
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batch_shape = torch.Size()
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else:
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batch_shape = self.concentration.size()
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super(Gamma, self).__init__(batch_shape, validate_args=validate_args)
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def expand(self, batch_shape, _instance=None):
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new = self._get_checked_instance(Gamma, _instance)
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batch_shape = torch.Size(batch_shape)
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new.concentration = self.concentration.expand(batch_shape)
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new.rate = self.rate.expand(batch_shape)
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super(Gamma, new).__init__(batch_shape, validate_args=False)
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new._validate_args = self._validate_args
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return new
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def rsample(self, sample_shape=torch.Size()):
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shape = self._extended_shape(sample_shape)
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value = _standard_gamma(self.concentration.expand(shape)) / self.rate.expand(shape)
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value.detach().clamp_(min=torch.finfo(value.dtype).tiny) # do not record in autograd graph
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return value
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def log_prob(self, value):
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value = torch.as_tensor(value, dtype=self.rate.dtype, device=self.rate.device)
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if self._validate_args:
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self._validate_sample(value)
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return (self.concentration * torch.log(self.rate) +
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(self.concentration - 1) * torch.log(value) -
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self.rate * value - torch.lgamma(self.concentration))
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def entropy(self):
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return (self.concentration - torch.log(self.rate) + torch.lgamma(self.concentration) +
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(1.0 - self.concentration) * torch.digamma(self.concentration))
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@property
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def _natural_params(self):
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return (self.concentration - 1, -self.rate)
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def _log_normalizer(self, x, y):
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return torch.lgamma(x + 1) + (x + 1) * torch.log(-y.reciprocal())
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