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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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__all__ = ['Gamma'] |
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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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>>> # xdoctest: +IGNORE_WANT("non-deterinistic") |
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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.nonnegative |
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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 mode(self): |
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return ((self.concentration - 1) / self.rate).clamp(min=0) |
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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) |
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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 (torch.xlogy(self.concentration, self.rate) + |
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torch.xlogy(self.concentration - 1, 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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