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import torch |
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from torch import Tensor |
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from torch.distributions import constraints |
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from torch.distributions.dirichlet import Dirichlet |
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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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from torch.types import _Number, _size |
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__all__ = ["Beta"] |
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class Beta(ExponentialFamily): |
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r""" |
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Beta distribution parameterized by :attr:`concentration1` and :attr:`concentration0`. |
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Example:: |
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>>> # xdoctest: +IGNORE_WANT("non-deterministic") |
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>>> m = Beta(torch.tensor([0.5]), torch.tensor([0.5])) |
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>>> m.sample() # Beta distributed with concentration concentration1 and concentration0 |
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tensor([ 0.1046]) |
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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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if isinstance(concentration1, _Number) and isinstance(concentration0, _Number): |
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concentration1_concentration0 = torch.tensor( |
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[float(concentration1), float(concentration0)] |
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) |
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else: |
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concentration1, concentration0 = broadcast_all( |
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concentration1, concentration0 |
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) |
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concentration1_concentration0 = torch.stack( |
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[concentration1, concentration0], -1 |
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) |
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self._dirichlet = Dirichlet( |
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concentration1_concentration0, validate_args=validate_args |
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) |
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super().__init__(self._dirichlet._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(Beta, _instance) |
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batch_shape = torch.Size(batch_shape) |
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new._dirichlet = self._dirichlet.expand(batch_shape) |
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super(Beta, 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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@property |
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def mean(self) -> Tensor: |
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return self.concentration1 / (self.concentration1 + self.concentration0) |
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@property |
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def mode(self) -> Tensor: |
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return self._dirichlet.mode[..., 0] |
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@property |
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def variance(self) -> Tensor: |
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total = self.concentration1 + self.concentration0 |
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return self.concentration1 * self.concentration0 / (total.pow(2) * (total + 1)) |
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def rsample(self, sample_shape: _size = ()) -> Tensor: |
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return self._dirichlet.rsample(sample_shape).select(-1, 0) |
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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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heads_tails = torch.stack([value, 1.0 - value], -1) |
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return self._dirichlet.log_prob(heads_tails) |
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def entropy(self): |
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return self._dirichlet.entropy() |
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@property |
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def concentration1(self) -> Tensor: |
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result = self._dirichlet.concentration[..., 0] |
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if isinstance(result, _Number): |
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return torch.tensor([result]) |
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else: |
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return result |
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@property |
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def concentration0(self) -> Tensor: |
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result = self._dirichlet.concentration[..., 1] |
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if isinstance(result, _Number): |
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return torch.tensor([result]) |
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else: |
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return result |
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@property |
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def _natural_params(self) -> tuple[Tensor, Tensor]: |
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return (self.concentration1, self.concentration0) |
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def _log_normalizer(self, x, y): |
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return torch.lgamma(x) + torch.lgamma(y) - torch.lgamma(x + y) |
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