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# Source code for torch.distributions.studentT

import math

import torch
from torch._six import inf, nan
from torch.distributions import Chi2, constraints
from torch.distributions.distribution import Distribution

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

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