Source code for torch.distributions.transformed_distribution
# mypy: allow-untyped-defs
from typing import Dict
import torch
from torch.distributions import constraints
from torch.distributions.distribution import Distribution
from torch.distributions.independent import Independent
from torch.distributions.transforms import ComposeTransform, Transform
from torch.distributions.utils import _sum_rightmost
from torch.types import _size
__all__ = ["TransformedDistribution"]
[docs]class TransformedDistribution(Distribution):
r"""
Extension of the Distribution class, which applies a sequence of Transforms
to a base distribution. Let f be the composition of transforms applied::
X ~ BaseDistribution
Y = f(X) ~ TransformedDistribution(BaseDistribution, f)
log p(Y) = log p(X) + log |det (dX/dY)|
Note that the ``.event_shape`` of a :class:`TransformedDistribution` is the
maximum shape of its base distribution and its transforms, since transforms
can introduce correlations among events.
An example for the usage of :class:`TransformedDistribution` would be::
# Building a Logistic Distribution
# X ~ Uniform(0, 1)
# f = a + b * logit(X)
# Y ~ f(X) ~ Logistic(a, b)
base_distribution = Uniform(0, 1)
transforms = [SigmoidTransform().inv, AffineTransform(loc=a, scale=b)]
logistic = TransformedDistribution(base_distribution, transforms)
For more examples, please look at the implementations of
:class:`~torch.distributions.gumbel.Gumbel`,
:class:`~torch.distributions.half_cauchy.HalfCauchy`,
:class:`~torch.distributions.half_normal.HalfNormal`,
:class:`~torch.distributions.log_normal.LogNormal`,
:class:`~torch.distributions.pareto.Pareto`,
:class:`~torch.distributions.weibull.Weibull`,
:class:`~torch.distributions.relaxed_bernoulli.RelaxedBernoulli` and
:class:`~torch.distributions.relaxed_categorical.RelaxedOneHotCategorical`
"""
arg_constraints: Dict[str, constraints.Constraint] = {}
def __init__(self, base_distribution, transforms, validate_args=None):
if isinstance(transforms, Transform):
self.transforms = [
transforms,
]
elif isinstance(transforms, list):
if not all(isinstance(t, Transform) for t in transforms):
raise ValueError(
"transforms must be a Transform or a list of Transforms"
)
self.transforms = transforms
else:
raise ValueError(
f"transforms must be a Transform or list, but was {transforms}"
)
# Reshape base_distribution according to transforms.
base_shape = base_distribution.batch_shape + base_distribution.event_shape
base_event_dim = len(base_distribution.event_shape)
transform = ComposeTransform(self.transforms)
if len(base_shape) < transform.domain.event_dim:
raise ValueError(
f"base_distribution needs to have shape with size at least {transform.domain.event_dim}, but got {base_shape}."
)
forward_shape = transform.forward_shape(base_shape)
expanded_base_shape = transform.inverse_shape(forward_shape)
if base_shape != expanded_base_shape:
base_batch_shape = expanded_base_shape[
: len(expanded_base_shape) - base_event_dim
]
base_distribution = base_distribution.expand(base_batch_shape)
reinterpreted_batch_ndims = transform.domain.event_dim - base_event_dim
if reinterpreted_batch_ndims > 0:
base_distribution = Independent(
base_distribution, reinterpreted_batch_ndims
)
self.base_dist = base_distribution
# Compute shapes.
transform_change_in_event_dim = (
transform.codomain.event_dim - transform.domain.event_dim
)
event_dim = max(
transform.codomain.event_dim, # the transform is coupled
base_event_dim + transform_change_in_event_dim, # the base dist is coupled
)
assert len(forward_shape) >= event_dim
cut = len(forward_shape) - event_dim
batch_shape = forward_shape[:cut]
event_shape = forward_shape[cut:]
super().__init__(batch_shape, event_shape, validate_args=validate_args)
[docs] def expand(self, batch_shape, _instance=None):
new = self._get_checked_instance(TransformedDistribution, _instance)
batch_shape = torch.Size(batch_shape)
shape = batch_shape + self.event_shape
for t in reversed(self.transforms):
shape = t.inverse_shape(shape)
base_batch_shape = shape[: len(shape) - len(self.base_dist.event_shape)]
new.base_dist = self.base_dist.expand(base_batch_shape)
new.transforms = self.transforms
super(TransformedDistribution, new).__init__(
batch_shape, self.event_shape, validate_args=False
)
new._validate_args = self._validate_args
return new
@constraints.dependent_property(is_discrete=False)
def support(self):
if not self.transforms:
return self.base_dist.support
support = self.transforms[-1].codomain
if len(self.event_shape) > support.event_dim:
support = constraints.independent(
support, len(self.event_shape) - support.event_dim
)
return support
@property
def has_rsample(self):
return self.base_dist.has_rsample
[docs] def sample(self, sample_shape=torch.Size()):
"""
Generates a sample_shape shaped sample or sample_shape shaped batch of
samples if the distribution parameters are batched. Samples first from
base distribution and applies `transform()` for every transform in the
list.
"""
with torch.no_grad():
x = self.base_dist.sample(sample_shape)
for transform in self.transforms:
x = transform(x)
return x
[docs] def rsample(self, sample_shape: _size = torch.Size()) -> torch.Tensor:
"""
Generates a sample_shape shaped reparameterized sample or sample_shape
shaped batch of reparameterized samples if the distribution parameters
are batched. Samples first from base distribution and applies
`transform()` for every transform in the list.
"""
x = self.base_dist.rsample(sample_shape)
for transform in self.transforms:
x = transform(x)
return x
[docs] def log_prob(self, value):
"""
Scores the sample by inverting the transform(s) and computing the score
using the score of the base distribution and the log abs det jacobian.
"""
if self._validate_args:
self._validate_sample(value)
event_dim = len(self.event_shape)
log_prob = 0.0
y = value
for transform in reversed(self.transforms):
x = transform.inv(y)
event_dim += transform.domain.event_dim - transform.codomain.event_dim
log_prob = log_prob - _sum_rightmost(
transform.log_abs_det_jacobian(x, y),
event_dim - transform.domain.event_dim,
)
y = x
log_prob = log_prob + _sum_rightmost(
self.base_dist.log_prob(y), event_dim - len(self.base_dist.event_shape)
)
return log_prob
def _monotonize_cdf(self, value):
"""
This conditionally flips ``value -> 1-value`` to ensure :meth:`cdf` is
monotone increasing.
"""
sign = 1
for transform in self.transforms:
sign = sign * transform.sign
if isinstance(sign, int) and sign == 1:
return value
return sign * (value - 0.5) + 0.5
[docs] def cdf(self, value):
"""
Computes the cumulative distribution function by inverting the
transform(s) and computing the score of the base distribution.
"""
for transform in self.transforms[::-1]:
value = transform.inv(value)
if self._validate_args:
self.base_dist._validate_sample(value)
value = self.base_dist.cdf(value)
value = self._monotonize_cdf(value)
return value
[docs] def icdf(self, value):
"""
Computes the inverse cumulative distribution function using
transform(s) and computing the score of the base distribution.
"""
value = self._monotonize_cdf(value)
value = self.base_dist.icdf(value)
for transform in self.transforms:
value = transform(value)
return value
