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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__ = ["Poisson"] |
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class Poisson(ExponentialFamily): |
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r""" |
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Creates a Poisson distribution parameterized by :attr:`rate`, the rate parameter. |
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Samples are nonnegative integers, with a pmf given by |
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.. math:: |
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\mathrm{rate}^k \frac{e^{-\mathrm{rate}}}{k!} |
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Example:: |
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>>> # xdoctest: +SKIP("poisson_cpu not implemented for 'Long'") |
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>>> m = Poisson(torch.tensor([4])) |
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>>> m.sample() |
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tensor([ 3.]) |
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Args: |
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rate (Number, Tensor): the rate parameter |
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""" |
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arg_constraints = {"rate": constraints.nonnegative} |
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support = constraints.nonnegative_integer |
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@property |
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def mean(self): |
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return self.rate |
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@property |
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def mode(self): |
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return self.rate.floor() |
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@property |
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def variance(self): |
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return self.rate |
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def __init__(self, rate, validate_args=None): |
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(self.rate,) = broadcast_all(rate) |
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if isinstance(rate, Number): |
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batch_shape = torch.Size() |
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else: |
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batch_shape = self.rate.size() |
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super().__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(Poisson, _instance) |
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batch_shape = torch.Size(batch_shape) |
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new.rate = self.rate.expand(batch_shape) |
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super(Poisson, 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 sample(self, sample_shape=torch.Size()): |
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shape = self._extended_shape(sample_shape) |
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with torch.no_grad(): |
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return torch.poisson(self.rate.expand(shape)) |
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def log_prob(self, value): |
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if self._validate_args: |
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self._validate_sample(value) |
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rate, value = broadcast_all(self.rate, value) |
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return value.xlogy(rate) - rate - (value + 1).lgamma() |
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@property |
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def _natural_params(self): |
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return (torch.log(self.rate),) |
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def _log_normalizer(self, x): |
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return torch.exp(x) |
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