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