# Copyright Contributors to the Pyro project. # SPDX-License-Identifier: Apache-2.0 # The implementation follows the design in PyTorch: torch.distributions.distribution.py # # Copyright (c) 2016- Facebook, Inc (Adam Paszke) # Copyright (c) 2014- Facebook, Inc (Soumith Chintala) # Copyright (c) 2011-2014 Idiap Research Institute (Ronan Collobert) # Copyright (c) 2012-2014 Deepmind Technologies (Koray Kavukcuoglu) # Copyright (c) 2011-2012 NEC Laboratories America (Koray Kavukcuoglu) # Copyright (c) 2011-2013 NYU (Clement Farabet) # Copyright (c) 2006-2010 NEC Laboratories America (Ronan Collobert, Leon Bottou, Iain Melvin, Jason Weston) # Copyright (c) 2006 Idiap Research Institute (Samy Bengio) # Copyright (c) 2001-2004 Idiap Research Institute (Ronan Collobert, Samy Bengio, Johnny Mariethoz) # # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" # AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE # IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE # ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE # LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR # CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF # SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS # INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN # CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) # ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE # POSSIBILITY OF SUCH DAMAGE. from collections import OrderedDict from contextlib import contextmanager import functools import inspect import warnings import numpy as np from jax import lax, tree_util import jax.numpy as jnp from jax.scipy.special import logsumexp from numpyro.distributions.transforms import AbsTransform, ComposeTransform, Transform from numpyro.distributions.util import ( lazy_property, promote_shapes, sum_rightmost, validate_sample, ) from numpyro.util import find_stack_level, not_jax_tracer from . import constraints _VALIDATION_ENABLED = False def enable_validation(is_validate=True): """ Enable or disable validation checks in NumPyro. Validation checks provide useful warnings and errors, e.g. NaN checks, validating distribution arguments and support values, etc. which is useful for debugging. .. note:: This utility does not take effect under JAX's JIT compilation or vectorized transformation :func:`jax.vmap`. :param bool is_validate: whether to enable validation checks. """ global _VALIDATION_ENABLED _VALIDATION_ENABLED = is_validate Distribution.set_default_validate_args(is_validate) @contextmanager def validation_enabled(is_validate=True): """ Context manager that is useful when temporarily enabling/disabling validation checks. :param bool is_validate: whether to enable validation checks. """ distribution_validation_status = _VALIDATION_ENABLED try: enable_validation(is_validate) yield finally: enable_validation(distribution_validation_status) COERCIONS = [] class DistributionMeta(type): def __init__(cls, *args, **kwargs): signature = inspect.signature(functools.partial(cls.__init__, None)) cls.__signature__ = signature return super().__init__(*args, **kwargs) def __call__(cls, *args, **kwargs): for coerce_ in COERCIONS: result = coerce_(cls, args, kwargs) if result is not None: return result return super().__call__(*args, **kwargs) class Distribution(metaclass=DistributionMeta): """ Base class for probability distributions in NumPyro. The design largely follows from :mod:`torch.distributions`. :param batch_shape: The batch shape for the distribution. This designates independent (possibly non-identical) dimensions of a sample from the distribution. This is fixed for a distribution instance and is inferred from the shape of the distribution parameters. :param event_shape: The event shape for the distribution. This designates the dependent dimensions of a sample from the distribution. These are collapsed when we evaluate the log probability density of a batch of samples using `.log_prob`. :param validate_args: Whether to enable validation of distribution parameters and arguments to `.log_prob` method. As an example: .. doctest:: >>> import jax.numpy as jnp >>> import numpyro.distributions as dist >>> d = dist.Dirichlet(jnp.ones((2, 3, 4))) >>> d.batch_shape (2, 3) >>> d.event_shape (4,) """ arg_constraints = {} support = None has_enumerate_support = False reparametrized_params = [] _validate_args = False # register Distribution as a pytree # ref: https://github.com/google/jax/issues/2916 def __init_subclass__(cls, **kwargs): super().__init_subclass__(**kwargs) tree_util.register_pytree_node(cls, cls.tree_flatten, cls.tree_unflatten) def tree_flatten(self): return ( tuple( getattr(self, param) for param in sorted(self.arg_constraints.keys()) ), None, ) @classmethod def tree_unflatten(cls, aux_data, params): return cls(**dict(zip(sorted(cls.arg_constraints.keys()), params))) @staticmethod def set_default_validate_args(value): if value not in [True, False]: raise ValueError Distribution._validate_args = value def __init__(self, batch_shape=(), event_shape=(), *, validate_args=None): self._batch_shape = batch_shape self._event_shape = event_shape if validate_args is not None: self._validate_args = validate_args if self._validate_args: for param, constraint in self.arg_constraints.items(): if param not in self.__dict__ and isinstance( getattr(type(self), param), lazy_property ): continue if constraints.is_dependent(constraint): continue # skip constraints that cannot be checked is_valid = constraint(getattr(self, param)) if not_jax_tracer(is_valid): if not np.all(is_valid): raise ValueError( "{} distribution got invalid {} parameter.".format( self.__class__.__name__, param ) ) super(Distribution, self).__init__() @property def batch_shape(self): """ Returns the shape over which the distribution parameters are batched. :return: batch shape of the distribution. :rtype: tuple """ return self._batch_shape @property def event_shape(self): """ Returns the shape of a single sample from the distribution without batching. :return: event shape of the distribution. :rtype: tuple """ return self._event_shape @property def event_dim(self): """ :return: Number of dimensions of individual events. :rtype: int """ return len(self.event_shape) @property def has_rsample(self): return set(self.reparametrized_params) == set(self.arg_constraints) def rsample(self, key, sample_shape=()): if self.has_rsample: return self.sample(key, sample_shape=sample_shape) raise NotImplementedError def shape(self, sample_shape=()): """ The tensor shape of samples from this distribution. Samples are of shape:: d.shape(sample_shape) == sample_shape + d.batch_shape + d.event_shape :param tuple sample_shape: the size of the iid batch to be drawn from the distribution. :return: shape of samples. :rtype: tuple """ return sample_shape + self.batch_shape + self.event_shape def sample(self, key, sample_shape=()): """ Returns a sample from the distribution having shape given by `sample_shape + batch_shape + event_shape`. Note that when `sample_shape` is non-empty, leading dimensions (of size `sample_shape`) of the returned sample will be filled with iid draws from the distribution instance. :param jax.random.PRNGKey key: the rng_key key to be used for the distribution. :param tuple sample_shape: the sample shape for the distribution. :return: an array of shape `sample_shape + batch_shape + event_shape` :rtype: numpy.ndarray """ raise NotImplementedError def sample_with_intermediates(self, key, sample_shape=()): """ Same as ``sample`` except that any intermediate computations are returned (useful for `TransformedDistribution`). :param jax.random.PRNGKey key: the rng_key key to be used for the distribution. :param tuple sample_shape: the sample shape for the distribution. :return: an array of shape `sample_shape + batch_shape + event_shape` :rtype: numpy.ndarray """ return self.sample(key, sample_shape=sample_shape), [] def log_prob(self, value): """ Evaluates the log probability density for a batch of samples given by `value`. :param value: A batch of samples from the distribution. :return: an array with shape `value.shape[:-self.event_shape]` :rtype: numpy.ndarray """ raise NotImplementedError @property def mean(self): """ Mean of the distribution. """ raise NotImplementedError @property def variance(self): """ Variance of the distribution. """ raise NotImplementedError def _validate_sample(self, value): mask = self.support(value) if not_jax_tracer(mask): if not np.all(mask): warnings.warn( "Out-of-support values provided to log prob method. " "The value argument should be within the support.", stacklevel=find_stack_level(), ) return mask def __call__(self, *args, **kwargs): key = kwargs.pop("rng_key") sample_intermediates = kwargs.pop("sample_intermediates", False) if sample_intermediates: return self.sample_with_intermediates(key, *args, **kwargs) return self.sample(key, *args, **kwargs) def to_event(self, reinterpreted_batch_ndims=None): """ Interpret the rightmost `reinterpreted_batch_ndims` batch dimensions as dependent event dimensions. :param reinterpreted_batch_ndims: Number of rightmost batch dims to interpret as event dims. :return: An instance of `Independent` distribution. :rtype: numpyro.distributions.distribution.Independent """ if reinterpreted_batch_ndims is None: reinterpreted_batch_ndims = len(self.batch_shape) if reinterpreted_batch_ndims == 0: return self return Independent(self, reinterpreted_batch_ndims) def enumerate_support(self, expand=True): """ Returns an array with shape `len(support) x batch_shape` containing all values in the support. """ raise NotImplementedError def expand(self, batch_shape): """ Returns a new :class:`ExpandedDistribution` instance with batch dimensions expanded to `batch_shape`. :param tuple batch_shape: batch shape to expand to. :return: an instance of `ExpandedDistribution`. :rtype: :class:`ExpandedDistribution` """ batch_shape = tuple(batch_shape) if batch_shape == self.batch_shape: return self return ExpandedDistribution(self, batch_shape) def expand_by(self, sample_shape): """ Expands a distribution by adding ``sample_shape`` to the left side of its :attr:`~numpyro.distributions.distribution.Distribution.batch_shape`. To expand internal dims of ``self.batch_shape`` from 1 to something larger, use :meth:`expand` instead. :param tuple sample_shape: The size of the iid batch to be drawn from the distribution. :return: An expanded version of this distribution. :rtype: :class:`ExpandedDistribution` """ return self.expand(tuple(sample_shape) + self.batch_shape) def mask(self, mask): """ Masks a distribution by a boolean or boolean-valued array that is broadcastable to the distributions :attr:`Distribution.batch_shape` . :param mask: A boolean or boolean valued array (`True` includes a site, `False` excludes a site). :type mask: bool or jnp.ndarray :return: A masked copy of this distribution. :rtype: :class:`MaskedDistribution` **Example:** .. doctest:: >>> from jax import random >>> import jax.numpy as jnp >>> import numpyro >>> import numpyro.distributions as dist >>> from numpyro.distributions import constraints >>> from numpyro.infer import SVI, Trace_ELBO >>> def model(data, m): ... f = numpyro.sample("latent_fairness", dist.Beta(1, 1)) ... with numpyro.plate("N", data.shape[0]): ... # only take into account the values selected by the mask ... masked_dist = dist.Bernoulli(f).mask(m) ... numpyro.sample("obs", masked_dist, obs=data) >>> def guide(data, m): ... alpha_q = numpyro.param("alpha_q", 5., constraint=constraints.positive) ... beta_q = numpyro.param("beta_q", 5., constraint=constraints.positive) ... numpyro.sample("latent_fairness", dist.Beta(alpha_q, beta_q)) >>> data = jnp.concatenate([jnp.ones(5), jnp.zeros(5)]) >>> # select values equal to one >>> masked_array = jnp.where(data == 1, True, False) >>> optimizer = numpyro.optim.Adam(step_size=0.05) >>> svi = SVI(model, guide, optimizer, loss=Trace_ELBO()) >>> svi_result = svi.run(random.PRNGKey(0), 300, data, masked_array) >>> params = svi_result.params >>> # inferred_mean is closer to 1 >>> inferred_mean = params["alpha_q"] / (params["alpha_q"] + params["beta_q"]) """ if mask is True: return self return MaskedDistribution(self, mask) @classmethod def infer_shapes(cls, *args, **kwargs): r""" Infers ``batch_shape`` and ``event_shape`` given shapes of args to :meth:`__init__`. .. note:: This assumes distribution shape depends only on the shapes of tensor inputs, not in the data contained in those inputs. :param \*args: Positional args replacing each input arg with a tuple representing the sizes of each tensor input. :param \*\*kwargs: Keywords mapping name of input arg to tuple representing the sizes of each tensor input. :returns: A pair ``(batch_shape, event_shape)`` of the shapes of a distribution that would be created with input args of the given shapes. :rtype: tuple """ if cls.support.event_dim > 0: raise NotImplementedError # Convert args to kwargs. try: arg_names = cls._arg_names except AttributeError: sig = inspect.signature(cls.__init__) arg_names = cls._arg_names = tuple(sig.parameters)[1:] kwargs.update(zip(arg_names, args)) # Assumes distribution is univariate. batch_shapes = [] for name, shape in kwargs.items(): event_dim = cls.arg_constraints.get(name, constraints.real).event_dim batch_shapes.append(shape[: len(shape) - event_dim]) batch_shape = lax.broadcast_shapes(*batch_shapes) if batch_shapes else () event_shape = () return batch_shape, event_shape def cdf(self, value): """ The cummulative distribution function of this distribution. :param value: samples from this distribution. :return: output of the cummulative distribution function evaluated at `value`. """ raise NotImplementedError def icdf(self, q): """ The inverse cumulative distribution function of this distribution. :param q: quantile values, should belong to [0, 1]. :return: the samples whose cdf values equals to `q`. """ raise NotImplementedError @property def is_discrete(self): return self.support.is_discrete class ExpandedDistribution(Distribution): arg_constraints = {} def __init__(self, base_dist, batch_shape=()): if isinstance(base_dist, ExpandedDistribution): batch_shape, _, _ = self._broadcast_shape( base_dist.batch_shape, batch_shape ) base_dist = base_dist.base_dist self.base_dist = base_dist # adjust batch shape # Do basic validation. e.g. we should not "unexpand" distributions even if that is possible. new_shape, _, _ = self._broadcast_shape(base_dist.batch_shape, batch_shape) # Record interstitial and expanded dims/sizes w.r.t. the base distribution new_shape, expanded_sizes, interstitial_sizes = self._broadcast_shape( base_dist.batch_shape, new_shape ) self._expanded_sizes = expanded_sizes self._interstitial_sizes = interstitial_sizes super().__init__(new_shape, base_dist.event_shape) @staticmethod def _broadcast_shape(existing_shape, new_shape): if len(new_shape) < len(existing_shape): raise ValueError( "Cannot broadcast distribution of shape {} to shape {}".format( existing_shape, new_shape ) ) reversed_shape = list(reversed(existing_shape)) expanded_sizes, interstitial_sizes = [], [] for i, size in enumerate(reversed(new_shape)): if i >= len(reversed_shape): reversed_shape.append(size) expanded_sizes.append((-i - 1, size)) elif reversed_shape[i] == 1: if size != 1: reversed_shape[i] = size interstitial_sizes.append((-i - 1, size)) elif reversed_shape[i] != size: raise ValueError( "Cannot broadcast distribution of shape {} to shape {}".format( existing_shape, new_shape ) ) return ( tuple(reversed(reversed_shape)), OrderedDict(expanded_sizes), OrderedDict(interstitial_sizes), ) @property def has_enumerate_support(self): return self.base_dist.has_enumerate_support @property def has_rsample(self): return self.base_dist.has_rsample def _sample(self, sample_fn, key, sample_shape=()): interstitial_sizes = tuple(self._interstitial_sizes.values()) expanded_sizes = tuple(self._expanded_sizes.values()) batch_shape = expanded_sizes + interstitial_sizes # shape = sample_shape + expanded_sizes + interstitial_sizes + base_dist.shape() samples, intermediates = sample_fn(key, sample_shape=sample_shape + batch_shape) interstitial_dims = tuple(self._interstitial_sizes.keys()) event_dim = len(self.event_shape) batch_ndims = jnp.ndim(samples) - event_dim interstitial_dims = tuple(batch_ndims + i for i in interstitial_dims) interstitial_idx = len(sample_shape) + len(expanded_sizes) interstitial_sample_dims = range( interstitial_idx, interstitial_idx + len(interstitial_dims) ) permutation = list(range(batch_ndims)) for dim1, dim2 in zip(interstitial_dims, interstitial_sample_dims): permutation[dim1], permutation[dim2] = permutation[dim2], permutation[dim1] def reshape_sample(x): """ Reshapes samples and intermediates to ensure that the output shape is correct: This implicitly replaces the interstitial dims of size 1 in the original batch_shape of base_dist with those in the expanded dims. """ x = jnp.transpose(x, permutation + list(range(batch_ndims, jnp.ndim(x)))) event_shape = jnp.shape(x)[batch_ndims:] return x.reshape(sample_shape + self.batch_shape + event_shape) intermediates = tree_util.tree_map(reshape_sample, intermediates) samples = reshape_sample(samples) return samples, intermediates def rsample(self, key, sample_shape=()): return self._sample( lambda *args, **kwargs: (self.base_dist.rsample(*args, **kwargs), []), key, sample_shape, )[0] @property def support(self): return self.base_dist.support def sample_with_intermediates(self, key, sample_shape=()): return self._sample(self.base_dist.sample_with_intermediates, key, sample_shape) def sample(self, key, sample_shape=()): return self.sample_with_intermediates(key, sample_shape)[0] def log_prob(self, value, intermediates=None): # TODO: utilize `intermediates` shape = lax.broadcast_shapes( self.batch_shape, jnp.shape(value)[: max(jnp.ndim(value) - self.event_dim, 0)], ) log_prob = self.base_dist.log_prob(value) return jnp.broadcast_to(log_prob, shape) def enumerate_support(self, expand=True): samples = self.base_dist.enumerate_support(expand=False) enum_shape = samples.shape[:1] samples = samples.reshape(enum_shape + (1,) * len(self.batch_shape)) if expand: samples = samples.expand(enum_shape + self.batch_shape) return samples @property def mean(self): return jnp.broadcast_to( self.base_dist.mean, self.batch_shape + self.event_shape ) @property def variance(self): return jnp.broadcast_to( self.base_dist.variance, self.batch_shape + self.event_shape ) def tree_flatten(self): prepend_ndim = len(self.batch_shape) - len(self.base_dist.batch_shape) base_dist = tree_util.tree_map( lambda x: promote_shapes(x, shape=(1,) * prepend_ndim + jnp.shape(x))[0], self.base_dist, ) base_flatten, base_aux = base_dist.tree_flatten() return base_flatten, (type(self.base_dist), base_aux, self.batch_shape) @classmethod def tree_unflatten(cls, aux_data, params): base_cls, base_aux, batch_shape = aux_data base_dist = base_cls.tree_unflatten(base_aux, params) prepend_shape = base_dist.batch_shape[ : len(base_dist.batch_shape) - len(batch_shape) ] return cls(base_dist, batch_shape=prepend_shape + batch_shape) class ImproperUniform(Distribution): """ A helper distribution with zero :meth:`log_prob` over the `support` domain. .. note:: `sample` method is not implemented for this distribution. In autoguide and mcmc, initial parameters for improper sites are derived from `init_to_uniform` or `init_to_value` strategies. **Usage:** .. doctest:: >>> from numpyro import sample >>> from numpyro.distributions import ImproperUniform, Normal, constraints >>> >>> def model(): ... # ordered vector with length 10 ... x = sample('x', ImproperUniform(constraints.ordered_vector, (), event_shape=(10,))) ... ... # real matrix with shape (3, 4) ... y = sample('y', ImproperUniform(constraints.real, (), event_shape=(3, 4))) ... ... # a shape-(6, 8) batch of length-5 vectors greater than 3 ... z = sample('z', ImproperUniform(constraints.greater_than(3), (6, 8), event_shape=(5,))) If you want to set improper prior over all values greater than `a`, where `a` is another random variable, you might use >>> def model(): ... a = sample('a', Normal(0, 1)) ... x = sample('x', ImproperUniform(constraints.greater_than(a), (), event_shape=())) or if you want to reparameterize it >>> from numpyro.distributions import TransformedDistribution, transforms >>> from numpyro.handlers import reparam >>> from numpyro.infer.reparam import TransformReparam >>> >>> def model(): ... a = sample('a', Normal(0, 1)) ... with reparam(config={'x': TransformReparam()}): ... x = sample('x', ... TransformedDistribution(ImproperUniform(constraints.positive, (), ()), ... transforms.AffineTransform(a, 1))) :param ~numpyro.distributions.constraints.Constraint support: the support of this distribution. :param tuple batch_shape: batch shape of this distribution. It is usually safe to set `batch_shape=()`. :param tuple event_shape: event shape of this distribution. """ arg_constraints = {} support = constraints.dependent def __init__(self, support, batch_shape, event_shape, *, validate_args=None): self.support = constraints.independent( support, len(event_shape) - support.event_dim ) super().__init__(batch_shape, event_shape, validate_args=validate_args) @validate_sample def log_prob(self, value): batch_shape = jnp.shape(value)[: jnp.ndim(value) - len(self.event_shape)] batch_shape = lax.broadcast_shapes(batch_shape, self.batch_shape) return jnp.zeros(batch_shape) def _validate_sample(self, value): mask = super(ImproperUniform, self)._validate_sample(value) batch_dim = jnp.ndim(value) - len(self.event_shape) if batch_dim < jnp.ndim(mask): mask = jnp.all(jnp.reshape(mask, jnp.shape(mask)[:batch_dim] + (-1,)), -1) return mask def tree_flatten(self): raise NotImplementedError( "Cannot flattening ImproperPrior distribution for general supports. " "Please raising a feature request for your specific `support`. " "Alternatively, you can use '.mask(False)' pattern. " "For example, to define an improper prior over positive domain, " "we can use the distribution `dist.LogNormal(0, 1).mask(False)`." ) class Independent(Distribution): """ Reinterprets batch dimensions of a distribution as event dims by shifting the batch-event dim boundary further to the left. From a practical standpoint, this is useful when changing the result of :meth:`log_prob`. For example, a univariate Normal distribution can be interpreted as a multivariate Normal with diagonal covariance: .. doctest:: >>> import numpyro.distributions as dist >>> normal = dist.Normal(jnp.zeros(3), jnp.ones(3)) >>> [normal.batch_shape, normal.event_shape] [(3,), ()] >>> diag_normal = dist.Independent(normal, 1) >>> [diag_normal.batch_shape, diag_normal.event_shape] [(), (3,)] :param numpyro.distribution.Distribution base_distribution: a distribution instance. :param int reinterpreted_batch_ndims: the number of batch dims to reinterpret as event dims. """ arg_constraints = {} def __init__(self, base_dist, reinterpreted_batch_ndims, *, validate_args=None): if reinterpreted_batch_ndims > len(base_dist.batch_shape): raise ValueError( "Expected reinterpreted_batch_ndims <= len(base_distribution.batch_shape), " "actual {} vs {}".format( reinterpreted_batch_ndims, len(base_dist.batch_shape) ) ) shape = base_dist.batch_shape + base_dist.event_shape event_dim = reinterpreted_batch_ndims + len(base_dist.event_shape) batch_shape = shape[: len(shape) - event_dim] event_shape = shape[len(shape) - event_dim :] self.base_dist = base_dist self.reinterpreted_batch_ndims = reinterpreted_batch_ndims super(Independent, self).__init__( batch_shape, event_shape, validate_args=validate_args ) @property def support(self): return constraints.independent( self.base_dist.support, self.reinterpreted_batch_ndims ) @property def has_enumerate_support(self): return self.base_dist.has_enumerate_support @property def reparametrized_params(self): return self.base_dist.reparametrized_params @property def mean(self): return self.base_dist.mean @property def variance(self): return self.base_dist.variance @property def has_rsample(self): return self.base_dist.has_rsample def rsample(self, key, sample_shape=()): return self.base_dist.rsample(key, sample_shape=sample_shape) def sample(self, key, sample_shape=()): return self.base_dist(rng_key=key, sample_shape=sample_shape) def log_prob(self, value): log_prob = self.base_dist.log_prob(value) return sum_rightmost(log_prob, self.reinterpreted_batch_ndims) def expand(self, batch_shape): base_batch_shape = ( batch_shape + self.event_shape[: self.reinterpreted_batch_ndims] ) return self.base_dist.expand(base_batch_shape).to_event( self.reinterpreted_batch_ndims ) def tree_flatten(self): base_flatten, base_aux = self.base_dist.tree_flatten() return base_flatten, ( type(self.base_dist), base_aux, self.reinterpreted_batch_ndims, ) @classmethod def tree_unflatten(cls, aux_data, params): base_cls, base_aux, reinterpreted_batch_ndims = aux_data base_dist = base_cls.tree_unflatten(base_aux, params) return cls(base_dist, reinterpreted_batch_ndims) class MaskedDistribution(Distribution): """ Masks a distribution by a boolean array that is broadcastable to the distribution's :attr:`Distribution.batch_shape`. In the special case ``mask is False``, computation of :meth:`log_prob` , is skipped, and constant zero values are returned instead. :param mask: A boolean or boolean-valued array. :type mask: jnp.ndarray or bool """ arg_constraints = {} def __init__(self, base_dist, mask): if isinstance(mask, bool): self._mask = mask else: batch_shape = lax.broadcast_shapes( jnp.shape(mask), tuple(base_dist.batch_shape) ) if mask.shape != batch_shape: mask = jnp.broadcast_to(mask, batch_shape) if base_dist.batch_shape != batch_shape: base_dist = base_dist.expand(batch_shape) self._mask = mask.astype("bool") self.base_dist = base_dist super().__init__(base_dist.batch_shape, base_dist.event_shape) @property def has_enumerate_support(self): return self.base_dist.has_enumerate_support @property def has_rsample(self): return self.base_dist.has_rsample def rsample(self, key, sample_shape=()): return self.base_dist.rsample(key, sample_shape=sample_shape) @property def support(self): return self.base_dist.support def sample(self, key, sample_shape=()): return self.base_dist(rng_key=key, sample_shape=sample_shape) def log_prob(self, value): if self._mask is False: shape = lax.broadcast_shapes( tuple(self.base_dist.batch_shape), jnp.shape(value)[: max(jnp.ndim(value) - len(self.event_shape), 0)], ) return jnp.zeros(shape) if self._mask is True: return self.base_dist.log_prob(value) try: default_value = self.base_dist.support.feasible_like(value) except NotImplementedError: pass else: mask = jnp.reshape( self._mask, jnp.shape(self._mask) + (1,) * self.event_dim ) value = jnp.where(mask, value, default_value) return jnp.where(self._mask, self.base_dist.log_prob(value), 0.0) def enumerate_support(self, expand=True): return self.base_dist.enumerate_support(expand=expand) @property def mean(self): return self.base_dist.mean @property def variance(self): return self.base_dist.variance def tree_flatten(self): base_flatten, base_aux = self.base_dist.tree_flatten() if isinstance(self._mask, bool): return base_flatten, (type(self.base_dist), base_aux, self._mask) else: return (base_flatten, self._mask), (type(self.base_dist), base_aux) @classmethod def tree_unflatten(cls, aux_data, params): if len(aux_data) == 2: base_flatten, mask = params base_cls, base_aux = aux_data else: base_flatten = params base_cls, base_aux, mask = aux_data base_dist = base_cls.tree_unflatten(base_aux, base_flatten) return cls(base_dist, mask) class TransformedDistribution(Distribution): """ Returns a distribution instance obtained as a result of applying a sequence of transforms to a base distribution. For an example, see :class:`~numpyro.distributions.LogNormal` and :class:`~numpyro.distributions.HalfNormal`. :param base_distribution: the base distribution over which to apply transforms. :param transforms: a single transform or a list of transforms. :param validate_args: Whether to enable validation of distribution parameters and arguments to `.log_prob` method. """ arg_constraints = {} def __init__(self, base_distribution, transforms, *, validate_args=None): if isinstance(transforms, Transform): 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" ) else: raise ValueError( "transforms must be a Transform or list, but was {}".format(transforms) ) if isinstance(base_distribution, TransformedDistribution): base_dist = base_distribution.base_dist self.transforms = base_distribution.transforms + transforms else: base_dist = base_distribution self.transforms = transforms base_shape = base_dist.shape() base_event_dim = base_dist.event_dim transform = ComposeTransform(self.transforms) domain_event_dim = transform.domain.event_dim if len(base_shape) < domain_event_dim: raise ValueError( "Base distribution needs to have shape with size at least {}, but got {}.".format( domain_event_dim, base_shape ) ) shape = transform.forward_shape(base_shape) expanded_base_shape = transform.inverse_shape(shape) if base_shape != expanded_base_shape: base_batch_shape = expanded_base_shape[ : len(expanded_base_shape) - base_event_dim ] base_dist = base_dist.expand(base_batch_shape) reinterpreted_batch_ndims = domain_event_dim - base_event_dim if reinterpreted_batch_ndims > 0: base_dist = base_dist.to_event(reinterpreted_batch_ndims) self.base_dist = base_dist # Compute shapes. event_dim = transform.codomain.event_dim + max( base_event_dim - domain_event_dim, 0 ) assert len(shape) >= event_dim cut = len(shape) - event_dim batch_shape = shape[:cut] event_shape = shape[cut:] super(TransformedDistribution, self).__init__( batch_shape, event_shape, validate_args=validate_args ) @property def has_rsample(self): return self.base_dist.has_rsample def rsample(self, key, sample_shape=()): x = self.base_dist.rsample(key, sample_shape=sample_shape) for transform in self.transforms: x = transform(x) return x @property def support(self): codomain = self.transforms[-1].codomain codomain_event_dim = codomain.event_dim assert self.event_dim >= codomain_event_dim if self.event_dim == codomain_event_dim: return codomain else: return constraints.independent( codomain, self.event_dim - codomain_event_dim ) def sample(self, key, sample_shape=()): x = self.base_dist(rng_key=key, sample_shape=sample_shape) for transform in self.transforms: x = transform(x) return x def sample_with_intermediates(self, key, sample_shape=()): x = self.base_dist(rng_key=key, sample_shape=sample_shape) intermediates = [] for transform in self.transforms: x_tmp = x x, t_inter = transform.call_with_intermediates(x) intermediates.append([x_tmp, t_inter]) return x, intermediates @validate_sample def log_prob(self, value, intermediates=None): if intermediates is not None: if len(intermediates) != len(self.transforms): raise ValueError( "Intermediates array has length = {}. Expected = {}.".format( len(intermediates), len(self.transforms) ) ) event_dim = len(self.event_shape) log_prob = 0.0 y = value for i, transform in enumerate(reversed(self.transforms)): x = transform.inv(y) if intermediates is None else intermediates[-i - 1][0] t_inter = None if intermediates is None else intermediates[-i - 1][1] t_log_det = transform.log_abs_det_jacobian(x, y, t_inter) batch_ndim = event_dim - transform.codomain.event_dim log_prob = log_prob - sum_rightmost(t_log_det, batch_ndim) event_dim = transform.domain.event_dim + batch_ndim 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 @property def mean(self): raise NotImplementedError @property def variance(self): raise NotImplementedError def tree_flatten(self): raise NotImplementedError( "Flatenning TransformedDistribution is only supported for some specific cases." " Consider using `TransformReparam` to convert this distribution to the base_dist," " which is supported in most situtations. In addition, please reach out to us with" " your usage cases." ) class FoldedDistribution(TransformedDistribution): """ Equivalent to ``TransformedDistribution(base_dist, AbsTransform())``, but additionally supports :meth:`log_prob` . :param Distribution base_dist: A univariate distribution to reflect. """ support = constraints.positive def __init__(self, base_dist, *, validate_args=None): if base_dist.event_shape: raise ValueError("Only univariate distributions can be folded.") super().__init__(base_dist, AbsTransform(), validate_args=validate_args) @validate_sample def log_prob(self, value): dim = max(len(self.batch_shape), jnp.ndim(value)) plus_minus = jnp.array([1.0, -1.0]).reshape((2,) + (1,) * dim) return logsumexp(self.base_dist.log_prob(plus_minus * value), axis=0) def tree_flatten(self): base_flatten, base_aux = self.base_dist.tree_flatten() return base_flatten, (type(self.base_dist), base_aux) @classmethod def tree_unflatten(cls, aux_data, params): base_cls, base_aux = aux_data base_dist = base_cls.tree_unflatten(base_aux, params) return cls(base_dist) class Delta(Distribution): arg_constraints = { "v": constraints.dependent(is_discrete=False), "log_density": constraints.real, } reparametrized_params = ["v", "log_density"] def __init__(self, v=0.0, log_density=0.0, event_dim=0, *, validate_args=None): if event_dim > jnp.ndim(v): raise ValueError( "Expected event_dim <= v.dim(), actual {} vs {}".format( event_dim, jnp.ndim(v) ) ) batch_dim = jnp.ndim(v) - event_dim batch_shape = jnp.shape(v)[:batch_dim] event_shape = jnp.shape(v)[batch_dim:] self.v = v # NB: following Pyro implementation, log_density should be broadcasted to batch_shape self.log_density = promote_shapes(log_density, shape=batch_shape)[0] super(Delta, self).__init__( batch_shape, event_shape, validate_args=validate_args ) @constraints.dependent_property def support(self): return constraints.independent(constraints.real, self.event_dim) def sample(self, key, sample_shape=()): shape = sample_shape + self.batch_shape + self.event_shape return jnp.broadcast_to(self.v, shape) @validate_sample def log_prob(self, value): log_prob = jnp.log(value == self.v) log_prob = sum_rightmost(log_prob, len(self.event_shape)) return log_prob + self.log_density @property def mean(self): return self.v @property def variance(self): return jnp.zeros(self.batch_shape + self.event_shape) def tree_flatten(self): return (self.v, self.log_density), self.event_dim @classmethod def tree_unflatten(cls, aux_data, params): return cls(*params, event_dim=aux_data) class Unit(Distribution): """ Trivial nonnormalized distribution representing the unit type. The unit type has a single value with no data, i.e. ``value.size == 0``. This is used for :func:`numpyro.factor` statements. """ arg_constraints = {"log_factor": constraints.real} support = constraints.real def __init__(self, log_factor, *, validate_args=None): batch_shape = jnp.shape(log_factor) event_shape = (0,) # This satisfies .size == 0. self.log_factor = log_factor super(Unit, self).__init__( batch_shape, event_shape, validate_args=validate_args ) def sample(self, key, sample_shape=()): return jnp.empty(sample_shape + self.batch_shape + self.event_shape) def log_prob(self, value): shape = lax.broadcast_shapes(self.batch_shape, jnp.shape(value)[:-1]) return jnp.broadcast_to(self.log_factor, shape)