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# Source code for torch.distributions.mixture_same_family

import torch
from torch.distributions.distribution import Distribution
from torch.distributions import Categorical
from torch.distributions import constraints
from typing import Dict

[docs]class MixtureSameFamily(Distribution):
r"""
The MixtureSameFamily distribution implements a (batch of) mixture
distribution where all component are from different parameterizations of
the same distribution type. It is parameterized by a Categorical
"selecting distribution" (over k component) and a component
distribution, i.e., a Distribution with a rightmost batch shape
(equal to [k]) which indexes each (batch of) component.

Examples::

# Construct Gaussian Mixture Model in 1D consisting of 5 equally
# weighted normal distributions
>>> mix = D.Categorical(torch.ones(5,))
>>> comp = D.Normal(torch.randn(5,), torch.rand(5,))
>>> gmm = MixtureSameFamily(mix, comp)

# Construct Gaussian Mixture Modle in 2D consisting of 5 equally
# weighted bivariate normal distributions
>>> mix = D.Categorical(torch.ones(5,))
>>> comp = D.Independent(D.Normal(
torch.randn(5,2), torch.rand(5,2)), 1)
>>> gmm = MixtureSameFamily(mix, comp)

# Construct a batch of 3 Gaussian Mixture Models in 2D each
# consisting of 5 random weighted bivariate normal distributions
>>> mix = D.Categorical(torch.rand(3,5))
>>> comp = D.Independent(D.Normal(
torch.randn(3,5,2), torch.rand(3,5,2)), 1)
>>> gmm = MixtureSameFamily(mix, comp)

Args:
mixture_distribution: torch.distributions.Categorical-like
instance. Manages the probability of selecting component.
The number of categories must match the rightmost batch
dimension of the component_distribution. Must have either
scalar batch_shape or batch_shape matching
component_distribution.batch_shape[:-1]
component_distribution: torch.distributions.Distribution-like
instance. Right-most batch dimension indexes component.
"""
arg_constraints: Dict[str, constraints.Constraint] = {}
has_rsample = False

def __init__(self,
mixture_distribution,
component_distribution,
validate_args=None):
self._mixture_distribution = mixture_distribution
self._component_distribution = component_distribution

if not isinstance(self._mixture_distribution, Categorical):
raise ValueError(" The Mixture distribution needs to be an "
" instance of torch.distribtutions.Categorical")

if not isinstance(self._component_distribution, Distribution):
raise ValueError("The Component distribution need to be an "
"instance of torch.distributions.Distribution")

# Check that batch size matches
mdbs = self._mixture_distribution.batch_shape
cdbs = self._component_distribution.batch_shape[:-1]
for size1, size2 in zip(reversed(mdbs), reversed(cdbs)):
if size1 != 1 and size2 != 1 and size1 != size2:
raise ValueError("mixture_distribution.batch_shape ({0}) is not "
"compatible with component_distribution."
"batch_shape({1})".format(mdbs, cdbs))

# Check that the number of mixture component matches
km = self._mixture_distribution.logits.shape[-1]
kc = self._component_distribution.batch_shape[-1]
if km is not None and kc is not None and km != kc:
raise ValueError("mixture_distribution component ({0}) does not"
" equal component_distribution.batch_shape[-1]"
" ({1})".format(km, kc))
self._num_component = km

event_shape = self._component_distribution.event_shape
self._event_ndims = len(event_shape)
super(MixtureSameFamily, self).__init__(batch_shape=cdbs,
event_shape=event_shape,
validate_args=validate_args)

[docs]    def expand(self, batch_shape, _instance=None):
batch_shape = torch.Size(batch_shape)
batch_shape_comp = batch_shape + (self._num_component,)
new = self._get_checked_instance(MixtureSameFamily, _instance)
new._component_distribution = \
self._component_distribution.expand(batch_shape_comp)
new._mixture_distribution = \
self._mixture_distribution.expand(batch_shape)
new._num_component = self._num_component
new._event_ndims = self._event_ndims
event_shape = new._component_distribution.event_shape
super(MixtureSameFamily, new).__init__(batch_shape=batch_shape,
event_shape=event_shape,
validate_args=False)
new._validate_args = self._validate_args
return new

@constraints.dependent_property
def support(self):
# FIXME this may have the wrong shape when support contains batched
# parameters
return self._component_distribution.support

@property
def mixture_distribution(self):
return self._mixture_distribution

@property
def component_distribution(self):
return self._component_distribution

@property
def mean(self):
dim=-1 - self._event_ndims)  # [B, E]

@property
def variance(self):
# Law of total variance: Var(Y) = E[Var(Y|X)] + Var(E[Y|X])
mean_cond_var = torch.sum(probs * self.component_distribution.variance,
dim=-1 - self._event_ndims)
var_cond_mean = torch.sum(probs * (self.component_distribution.mean -
dim=-1 - self._event_ndims)
return mean_cond_var + var_cond_mean

[docs]    def cdf(self, x):
cdf_x = self.component_distribution.cdf(x)
mix_prob = self.mixture_distribution.probs

[docs]    def log_prob(self, x):
if self._validate_args:
self._validate_sample(x)
log_prob_x = self.component_distribution.log_prob(x)  # [S, B, k]
log_mix_prob = torch.log_softmax(self.mixture_distribution.logits,
dim=-1)  # [B, k]

[docs]    def sample(self, sample_shape=torch.Size()):
sample_len = len(sample_shape)
batch_len = len(self.batch_shape)
gather_dim = sample_len + batch_len
es = self.event_shape

# mixture samples [n, B]
mix_sample = self.mixture_distribution.sample(sample_shape)
mix_shape = mix_sample.shape

# component samples [n, B, k, E]
comp_samples = self.component_distribution.sample(sample_shape)

# Gather along the k dimension
mix_sample_r = mix_sample.reshape(
mix_shape + torch.Size([1] * (len(es) + 1)))
mix_sample_r = mix_sample_r.repeat(
torch.Size([1] * len(mix_shape)) + torch.Size([1]) + es)

samples = torch.gather(comp_samples, gather_dim, mix_sample_r)
return samples.squeeze(gather_dim)

return x.unsqueeze(-1 - self._event_ndims)

dist_batch_ndims = self.batch_shape.numel()
cat_batch_ndims = self.mixture_distribution.batch_shape.numel()
pad_ndims = 0 if cat_batch_ndims == 1 else \
dist_batch_ndims - cat_batch_ndims
xs = x.shape
x = x.reshape(xs[:-1] + torch.Size(pad_ndims * [1]) +
xs[-1:] + torch.Size(self._event_ndims * [1]))
return x

def __repr__(self):
args_string = '\n  {},\n  {}'.format(self.mixture_distribution,
self.component_distribution)
return 'MixtureSameFamily' + '(' + args_string + ')'


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