pytorch

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import math
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import torch
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from torch import inf, nan
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from torch.distributions import Chi2, constraints
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from torch.distributions.distribution import Distribution
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from torch.distributions.utils import _standard_normal, broadcast_all
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__all__ = ["StudentT"]
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class StudentT(Distribution):
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    r"""
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    Creates a Student's t-distribution parameterized by degree of
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    freedom :attr:`df`, mean :attr:`loc` and scale :attr:`scale`.
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    Example::
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        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
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        >>> m = StudentT(torch.tensor([2.0]))
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        >>> m.sample()  # Student's t-distributed with degrees of freedom=2
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        tensor([ 0.1046])
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    Args:
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        df (float or Tensor): degrees of freedom
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        loc (float or Tensor): mean of the distribution
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        scale (float or Tensor): scale of the distribution
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    """
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    arg_constraints = {
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        "df": constraints.positive,
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        "loc": constraints.real,
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        "scale": constraints.positive,
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    }
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    support = constraints.real
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    has_rsample = True
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    @property
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    def mean(self):
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        m = self.loc.clone(memory_format=torch.contiguous_format)
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        m[self.df <= 1] = nan
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        return m
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    @property
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    def mode(self):
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        return self.loc
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    @property
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    def variance(self):
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        m = self.df.clone(memory_format=torch.contiguous_format)
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        m[self.df > 2] = (
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            self.scale[self.df > 2].pow(2)
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            * self.df[self.df > 2]
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            / (self.df[self.df > 2] - 2)
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        )
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        m[(self.df <= 2) & (self.df > 1)] = inf
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        m[self.df <= 1] = nan
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        return m
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    def __init__(self, df, loc=0.0, scale=1.0, validate_args=None):
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        self.df, self.loc, self.scale = broadcast_all(df, loc, scale)
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        self._chi2 = Chi2(self.df)
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        batch_shape = self.df.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(StudentT, _instance)
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        batch_shape = torch.Size(batch_shape)
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        new.df = self.df.expand(batch_shape)
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        new.loc = self.loc.expand(batch_shape)
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        new.scale = self.scale.expand(batch_shape)
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        new._chi2 = self._chi2.expand(batch_shape)
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        super(StudentT, 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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        # NOTE: This does not agree with scipy implementation as much as other distributions.
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        # (see https://github.com/fritzo/notebooks/blob/master/debug-student-t.ipynb). Using DoubleTensor
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        # parameters seems to help.
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        #   X ~ Normal(0, 1)
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        #   Z ~ Chi2(df)
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        #   Y = X / sqrt(Z / df) ~ StudentT(df)
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        shape = self._extended_shape(sample_shape)
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        X = _standard_normal(shape, dtype=self.df.dtype, device=self.df.device)
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        Z = self._chi2.rsample(sample_shape)
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        Y = X * torch.rsqrt(Z / self.df)
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        return self.loc + self.scale * Y
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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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        y = (value - self.loc) / self.scale
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        Z = (
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            self.scale.log()
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            + 0.5 * self.df.log()
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            + 0.5 * math.log(math.pi)
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            + torch.lgamma(0.5 * self.df)
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            - torch.lgamma(0.5 * (self.df + 1.0))
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        )
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        return -0.5 * (self.df + 1.0) * torch.log1p(y**2.0 / self.df) - Z
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    def entropy(self):
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        lbeta = (
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            torch.lgamma(0.5 * self.df)
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            + math.lgamma(0.5)
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            - torch.lgamma(0.5 * (self.df + 1))
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        )
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        return (
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            self.scale.log()
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            + 0.5
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            * (self.df + 1)
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            * (torch.digamma(0.5 * (self.df + 1)) - torch.digamma(0.5 * self.df))
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            + 0.5 * self.df.log()
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            + lbeta
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        )
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