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117 lines
3.8 KiB
117 lines
3.8 KiB
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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