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import torch
from torch.autograd import Function
from torch.autograd.function import once_differentiable
from torch.distributions import constraints
from torch.distributions.exp_family import ExponentialFamily
__all__ = ["Dirichlet"]
# This helper is exposed for testing.
def _Dirichlet_backward(x, concentration, grad_output):
total = concentration.sum(-1, True).expand_as(concentration)
grad = torch._dirichlet_grad(x, concentration, total)
return grad * (grad_output - (x * grad_output).sum(-1, True))
class _Dirichlet(Function):
@staticmethod
def forward(ctx, concentration):
x = torch._sample_dirichlet(concentration)
ctx.save_for_backward(x, concentration)
return x
@staticmethod
@once_differentiable
def backward(ctx, grad_output):
x, concentration = ctx.saved_tensors
return _Dirichlet_backward(x, concentration, grad_output)
class Dirichlet(ExponentialFamily):
r"""
Creates a Dirichlet distribution parameterized by concentration :attr:`concentration`.
Example::
>>> # xdoctest: +IGNORE_WANT("non-deterministic")
>>> m = Dirichlet(torch.tensor([0.5, 0.5]))
>>> m.sample() # Dirichlet distributed with concentration [0.5, 0.5]
tensor([ 0.1046, 0.8954])
Args:
concentration (Tensor): concentration parameter of the distribution
(often referred to as alpha)
"""
arg_constraints = {
"concentration": constraints.independent(constraints.positive, 1)
}
support = constraints.simplex
has_rsample = True
def __init__(self, concentration, validate_args=None):
if concentration.dim() < 1:
raise ValueError(
"`concentration` parameter must be at least one-dimensional."
)
self.concentration = concentration
batch_shape, event_shape = concentration.shape[:-1], concentration.shape[-1:]
super().__init__(batch_shape, event_shape, validate_args=validate_args)
def expand(self, batch_shape, _instance=None):
new = self._get_checked_instance(Dirichlet, _instance)
batch_shape = torch.Size(batch_shape)
new.concentration = self.concentration.expand(batch_shape + self.event_shape)
super(Dirichlet, new).__init__(
batch_shape, self.event_shape, validate_args=False
)
new._validate_args = self._validate_args
return new
def rsample(self, sample_shape=()):
shape = self._extended_shape(sample_shape)
concentration = self.concentration.expand(shape)
return _Dirichlet.apply(concentration)
def log_prob(self, value):
if self._validate_args:
self._validate_sample(value)
return (
torch.xlogy(self.concentration - 1.0, value).sum(-1)
+ torch.lgamma(self.concentration.sum(-1))
- torch.lgamma(self.concentration).sum(-1)
)
@property
def mean(self):
return self.concentration / self.concentration.sum(-1, True)
@property
def mode(self):
concentrationm1 = (self.concentration - 1).clamp(min=0.0)
mode = concentrationm1 / concentrationm1.sum(-1, True)
mask = (self.concentration < 1).all(axis=-1)
mode[mask] = torch.nn.functional.one_hot(
mode[mask].argmax(axis=-1), concentrationm1.shape[-1]
).to(mode)
return mode
@property
def variance(self):
con0 = self.concentration.sum(-1, True)
return (
self.concentration
* (con0 - self.concentration)
/ (con0.pow(2) * (con0 + 1))
)
def entropy(self):
k = self.concentration.size(-1)
a0 = self.concentration.sum(-1)
return (
torch.lgamma(self.concentration).sum(-1)
- torch.lgamma(a0)
- (k - a0) * torch.digamma(a0)
- ((self.concentration - 1.0) * torch.digamma(self.concentration)).sum(-1)
)
@property
def _natural_params(self):
return (self.concentration,)
def _log_normalizer(self, x):
return x.lgamma().sum(-1) - torch.lgamma(x.sum(-1))
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