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import math |
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import torch |
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from torch._six 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-deterinistic") |
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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 = {'df': constraints.positive, 'loc': constraints.real, 'scale': constraints.positive} |
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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] = self.scale[self.df > 2].pow(2) * self.df[self.df > 2] / (self.df[self.df > 2] - 2) |
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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., scale=1., 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(StudentT, self).__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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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 = (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.))) |
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return -0.5 * (self.df + 1.) * torch.log1p(y**2. / self.df) - Z |
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def entropy(self): |
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lbeta = torch.lgamma(0.5 * self.df) + math.lgamma(0.5) - torch.lgamma(0.5 * (self.df + 1)) |
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return (self.scale.log() + |
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0.5 * (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() + lbeta) |
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