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import math
import torch
from torch import inf, nan
from torch.distributions import Chi2, constraints
from torch.distributions.distribution import Distribution
from torch.distributions.utils import _standard_normal, broadcast_all
__all__ = ["StudentT"]
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::
>>> # xdoctest: +IGNORE_WANT("non-deterministic")
>>> 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(memory_format=torch.contiguous_format)
m[self.df <= 1] = nan
return m
@property
def mode(self):
return self.loc
@property
def variance(self):
m = self.df.clone(memory_format=torch.contiguous_format)
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=0.0, scale=1.0, 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().__init__(batch_shape, validate_args=validate_args)
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
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
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 + 1.0))
)
return -0.5 * (self.df + 1.0) * torch.log1p(y**2.0 / self.df) - Z
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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