Source code for pymc.distributions.distribution

#   Copyright 2020 The PyMC Developers
#
#   Licensed under the Apache License, Version 2.0 (the "License");
#   you may not use this file except in compliance with the License.
#   You may obtain a copy of the License at
#
#       http://www.apache.org/licenses/LICENSE-2.0
#
#   Unless required by applicable law or agreed to in writing, software
#   distributed under the License is distributed on an "AS IS" BASIS,
#   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
#   See the License for the specific language governing permissions and
#   limitations under the License.
import contextvars
import functools
import sys
import types
import warnings

from abc import ABCMeta
from functools import singledispatch
from typing import Callable, Optional, Sequence, Tuple, Union

import numpy as np

from aeppl.abstract import MeasurableVariable, _get_measurable_outputs
from aeppl.logprob import _logcdf, _logprob
from aeppl.rewriting import logprob_rewrites_db
from aesara import tensor as at
from aesara.compile.builders import OpFromGraph
from aesara.graph import node_rewriter
from aesara.graph.basic import Node, clone_replace
from aesara.graph.rewriting.basic import in2out
from aesara.graph.utils import MetaType
from aesara.tensor.basic import as_tensor_variable
from aesara.tensor.random.op import RandomVariable
from aesara.tensor.random.type import RandomType
from aesara.tensor.var import TensorVariable
from typing_extensions import TypeAlias

from pymc.aesaraf import convert_observed_data
from pymc.distributions.shape_utils import (
    Dims,
    Shape,
    convert_dims,
    convert_shape,
    convert_size,
    find_size,
    shape_from_dims,
)
from pymc.printing import str_for_dist
from pymc.util import UNSET
from pymc.vartypes import string_types

__all__ = [
    "DensityDistRV",
    "DensityDist",
    "Distribution",
    "Continuous",
    "Discrete",
    "SymbolicRandomVariable",
]

DIST_PARAMETER_TYPES: TypeAlias = Union[np.ndarray, int, float, TensorVariable]

vectorized_ppc = contextvars.ContextVar(
    "vectorized_ppc", default=None
)  # type: contextvars.ContextVar[Optional[Callable]]

PLATFORM = sys.platform


class _Unpickling:
    pass


class DistributionMeta(ABCMeta):
    """
    DistributionMeta class


    Notes
    -----
    DistributionMeta currently performs many functions, and will likely be refactored soon.
    See issue below for more details
    https://github.com/pymc-devs/pymc/issues/5308
    """

    def __new__(cls, name, bases, clsdict):

        # Forcefully deprecate old v3 `Distribution`s
        if "random" in clsdict:

            def _random(*args, **kwargs):
                warnings.warn(
                    "The old `Distribution.random` interface is deprecated.",
                    FutureWarning,
                    stacklevel=2,
                )
                return clsdict["random"](*args, **kwargs)

            clsdict["random"] = _random

        rv_op = clsdict.setdefault("rv_op", None)
        rv_type = None

        if isinstance(rv_op, RandomVariable):
            rv_type = type(rv_op)
            clsdict["rv_type"] = rv_type

        new_cls = super().__new__(cls, name, bases, clsdict)

        if rv_type is not None:
            # Create dispatch functions

            class_logp = clsdict.get("logp")
            if class_logp:

                @_logprob.register(rv_type)
                def logp(op, values, *dist_params, **kwargs):
                    dist_params = dist_params[3:]
                    (value,) = values
                    return class_logp(value, *dist_params)

            class_logcdf = clsdict.get("logcdf")
            if class_logcdf:

                @_logcdf.register(rv_type)
                def logcdf(op, value, *dist_params, **kwargs):
                    dist_params = dist_params[3:]
                    return class_logcdf(value, *dist_params)

            class_moment = clsdict.get("moment")
            if class_moment:

                @_moment.register(rv_type)
                def moment(op, rv, rng, size, dtype, *dist_params):
                    return class_moment(rv, size, *dist_params)

            # Register the Aesara `RandomVariable` type as a subclass of this
            # `Distribution` type.
            new_cls.register(rv_type)

        return new_cls


def _make_nice_attr_error(oldcode: str, newcode: str):
    def fn(*args, **kwargs):
        raise AttributeError(f"The `{oldcode}` method was removed. Instead use `{newcode}`.`")

    return fn


[docs]class SymbolicRandomVariable(OpFromGraph): """Symbolic Random Variable This is a subclasse of `OpFromGraph` which is used to encapsulate the symbolic random graph of complex distributions which are built on top of pure `RandomVariable`s. These graphs may vary structurally based on the inputs (e.g., their dimensionality), and usually require that random inputs have specific shapes for correct outputs (e.g., avoiding broadcasting of random inputs). Due to this, most distributions that return SymbolicRandomVariable create their these graphs at runtime via the classmethod `cls.rv_op`, taking care to clone and resize random inputs, if needed. """ ndim_supp: int = None """Number of support dimensions as in RandomVariables (0 for scalar, 1 for vector, ...) """ inline_aeppl: bool = False """Specifies whether the logprob function is derived automatically by introspection of the inner graph. If `False`, a logprob function must be dispatched directly to the subclass type. """ _print_name: Tuple[str, str] = ("Unknown", "\\operatorname{Unknown}") """Tuple of (name, latex name) used for for pretty-printing variables of this type"""
[docs] def __init__(self, *args, ndim_supp, **kwargs): self.ndim_supp = ndim_supp kwargs.setdefault("inline", True) super().__init__(*args, **kwargs)
[docs] def update(self, node: Node): """Symbolic update expression for input random state variables Returns a dictionary with the symbolic expressions required for correct updating of random state input variables repeated function evaluations. This is used by `aesaraf.compile_pymc`. """ return {}
[docs]class Distribution(metaclass=DistributionMeta): """Statistical distribution""" rv_op: [RandomVariable, SymbolicRandomVariable] = None rv_type: MetaType = None def __new__( cls, name: str, *args, rng=None, dims: Optional[Dims] = None, initval=None, observed=None, total_size=None, transform=UNSET, **kwargs, ) -> TensorVariable: """Adds a tensor variable corresponding to a PyMC distribution to the current model. Note that all remaining kwargs must be compatible with ``.dist()`` Parameters ---------- cls : type A PyMC distribution. name : str Name for the new model variable. rng : optional Random number generator to use with the RandomVariable. dims : tuple, optional A tuple of dimension names known to the model. When shape is not provided, the shape of dims is used to define the shape of the variable. initval : optional Numeric or symbolic untransformed initial value of matching shape, or one of the following initial value strategies: "moment", "prior". Depending on the sampler's settings, a random jitter may be added to numeric, symbolic or moment-based initial values in the transformed space. observed : optional Observed data to be passed when registering the random variable in the model. When neither shape nor dims is provided, the shape of observed is used to define the shape of the variable. See ``Model.register_rv``. total_size : float, optional See ``Model.register_rv``. transform : optional See ``Model.register_rv``. **kwargs Keyword arguments that will be forwarded to ``.dist()`` or the Aesara RV Op. Most prominently: ``shape`` for ``.dist()`` or ``dtype`` for the Op. Returns ------- rv : TensorVariable The created random variable tensor, registered in the Model. """ try: from pymc.model import Model model = Model.get_context() except TypeError: raise TypeError( "No model on context stack, which is needed to " "instantiate distributions. Add variable inside " "a 'with model:' block, or use the '.dist' syntax " "for a standalone distribution." ) if "testval" in kwargs: initval = kwargs.pop("testval") warnings.warn( "The `testval` argument is deprecated; use `initval`.", FutureWarning, stacklevel=2, ) if not isinstance(name, string_types): raise TypeError(f"Name needs to be a string but got: {name}") dims = convert_dims(dims) if observed is not None: observed = convert_observed_data(observed) # Preference is given to size or shape. If not specified, we rely on dims and # finally, observed, to determine the shape of the variable. if not ("size" in kwargs or "shape" in kwargs): if dims is not None: kwargs["shape"] = shape_from_dims(dims, model) elif observed is not None: kwargs["shape"] = tuple(observed.shape) rv_out = cls.dist(*args, **kwargs) rv_out = model.register_rv( rv_out, name, observed, total_size, dims=dims, transform=transform, initval=initval, ) # add in pretty-printing support rv_out.str_repr = types.MethodType(str_for_dist, rv_out) rv_out._repr_latex_ = types.MethodType( functools.partial(str_for_dist, formatting="latex"), rv_out ) rv_out.logp = _make_nice_attr_error("rv.logp(x)", "pm.logp(rv, x)") rv_out.logcdf = _make_nice_attr_error("rv.logcdf(x)", "pm.logcdf(rv, x)") rv_out.random = _make_nice_attr_error("rv.random()", "pm.draw(rv)") return rv_out
[docs] @classmethod def dist( cls, dist_params, *, shape: Optional[Shape] = None, **kwargs, ) -> TensorVariable: """Creates a tensor variable corresponding to the `cls` distribution. Parameters ---------- dist_params : array-like The inputs to the `RandomVariable` `Op`. shape : int, tuple, Variable, optional A tuple of sizes for each dimension of the new RV. **kwargs Keyword arguments that will be forwarded to the Aesara RV Op. Most prominently: ``size`` or ``dtype``. Returns ------- rv : TensorVariable The created random variable tensor. """ if "testval" in kwargs: kwargs.pop("testval") warnings.warn( "The `.dist(testval=...)` argument is deprecated and has no effect. " "Initial values for sampling/optimization can be specified with `initval` in a modelcontext. " "For using Aesara's test value features, you must assign the `.tag.test_value` yourself.", FutureWarning, stacklevel=2, ) if "initval" in kwargs: raise TypeError( "Unexpected keyword argument `initval`. " "This argument is not available for the `.dist()` API." ) if "dims" in kwargs: raise NotImplementedError("The use of a `.dist(dims=...)` API is not supported.") size = kwargs.pop("size", None) if shape is not None and size is not None: raise ValueError( f"Passing both `shape` ({shape}) and `size` ({size}) is not supported!" ) shape = convert_shape(shape) size = convert_size(size) # SymbolicRVs don't have `ndim_supp` until they are created ndim_supp = getattr(cls.rv_op, "ndim_supp", None) if ndim_supp is None: ndim_supp = cls.rv_op(*dist_params, **kwargs).owner.op.ndim_supp create_size = find_size(shape=shape, size=size, ndim_supp=ndim_supp) rv_out = cls.rv_op(*dist_params, size=create_size, **kwargs) rv_out.logp = _make_nice_attr_error("rv.logp(x)", "pm.logp(rv, x)") rv_out.logcdf = _make_nice_attr_error("rv.logcdf(x)", "pm.logcdf(rv, x)") rv_out.random = _make_nice_attr_error("rv.random()", "pm.draw(rv)") return rv_out
# Let Aeppl know that the SymbolicRandomVariable has a logprob. MeasurableVariable.register(SymbolicRandomVariable) @_get_measurable_outputs.register(SymbolicRandomVariable) def _get_measurable_outputs_symbolic_random_variable(op, node): # This tells Aeppl that any non RandomType outputs are measurable return [out for out in node.outputs if not isinstance(out.type, RandomType)] @node_rewriter([SymbolicRandomVariable]) def inline_symbolic_random_variable(fgraph, node): """ This optimization expands the internal graph of a SymbolicRV when obtaining logp from Aeppl, if the flag `inline_aeppl` is True. """ op = node.op if op.inline_aeppl: return clone_replace(op.inner_outputs, {u: v for u, v in zip(op.inner_inputs, node.inputs)}) # Registered before pre-canonicalization which happens at position=-10 logprob_rewrites_db.register( "inline_SymbolicRandomVariable", in2out(inline_symbolic_random_variable), "basic", position=-20, ) @singledispatch def _moment(op, rv, *rv_inputs) -> TensorVariable: raise NotImplementedError(f"Variable {rv} of type {op} has no moment implementation.") def moment(rv: TensorVariable) -> TensorVariable: """Method for choosing a representative point/value that can be used to start optimization or MCMC sampling. The only parameter to this function is the RandomVariable for which the value is to be derived. """ return _moment(rv.owner.op, rv, *rv.owner.inputs).astype(rv.dtype)
[docs]class Discrete(Distribution): """Base class for discrete distributions""" def __new__(cls, name, *args, **kwargs): if kwargs.get("transform", None): raise ValueError("Transformations for discrete distributions") return super().__new__(cls, name, *args, **kwargs)
[docs]class Continuous(Distribution): """Base class for continuous distributions"""
class DensityDistRV(RandomVariable): """ Base class for DensityDistRV This should be subclassed when defining custom DensityDist objects. """ name = "DensityDistRV" _print_name = ("DensityDist", "\\operatorname{DensityDist}") @classmethod def rng_fn(cls, rng, *args): args = list(args) size = args.pop(-1) return cls._random_fn(*args, rng=rng, size=size)
[docs]class DensityDist(Distribution): """A distribution that can be used to wrap black-box log density functions. Creates a Distribution and registers the supplied log density function to be used for inference. It is also possible to supply a `random` method in order to be able to sample from the prior or posterior predictive distributions. Parameters ---------- name : str dist_params : Tuple A sequence of the distribution's parameter. These will be converted into Aesara tensors internally. These parameters could be other ``TensorVariable`` instances created from , optionally created via ``RandomVariable`` ``Op``s. class_name : str Name for the RandomVariable class which will wrap the DensityDist methods. When not specified, it will be given the name of the variable. .. warning:: New DensityDists created with the same class_name will override the methods dispatched onto the previous classes. If using DensityDists with different methods across separate models, be sure to use distinct class_names. logp : Optional[Callable] A callable that calculates the log density of some given observed ``value`` conditioned on certain distribution parameter values. It must have the following signature: ``logp(value, *dist_params)``, where ``value`` is an Aesara tensor that represents the observed value, and ``dist_params`` are the tensors that hold the values of the distribution parameters. This function must return an Aesara tensor. If ``None``, a ``NotImplemented`` error will be raised when trying to compute the distribution's logp. logcdf : Optional[Callable] A callable that calculates the log cummulative probability of some given observed ``value`` conditioned on certain distribution parameter values. It must have the following signature: ``logcdf(value, *dist_params)``, where ``value`` is an Aesara tensor that represents the observed value, and ``dist_params`` are the tensors that hold the values of the distribution parameters. This function must return an Aesara tensor. If ``None``, a ``NotImplemented`` error will be raised when trying to compute the distribution's logcdf. random : Optional[Callable] A callable that can be used to generate random draws from the distribution. It must have the following signature: ``random(*dist_params, rng=None, size=None)``. The distribution parameters are passed as positional arguments in the same order as they are supplied when the ``DensityDist`` is constructed. The keyword arguments are ``rnd``, which will provide the random variable's associated :py:class:`~numpy.random.Generator`, and ``size``, that will represent the desired size of the random draw. If ``None``, a ``NotImplemented`` error will be raised when trying to draw random samples from the distribution's prior or posterior predictive. moment : Optional[Callable] A callable that can be used to compute the moments of the distribution. It must have the following signature: ``moment(rv, size, *rv_inputs)``. The distribution's :class:`~aesara.tensor.random.op.RandomVariable` is passed as the first argument ``rv``. ``size`` is the random variable's size implied by the ``dims``, ``size`` and parameters supplied to the distribution. Finally, ``rv_inputs`` is the sequence of the distribution parameters, in the same order as they were supplied when the DensityDist was created. If ``None``, a default ``moment`` function will be assigned that will always return 0, or an array of zeros. ndim_supp : int The number of dimensions in the support of the distribution. Defaults to assuming a scalar distribution, i.e. ``ndim_supp = 0``. ndims_params : Optional[Sequence[int]] The list of number of dimensions in the support of each of the distribution's parameters. If ``None``, it is assumed that all parameters are scalars, hence the number of dimensions of their support will be 0. dtype : str The dtype of the distribution. All draws and observations passed into the distribution will be casted onto this dtype. kwargs : Extra keyword arguments are passed to the parent's class ``__new__`` method. Examples -------- .. code-block:: python def logp(value, mu): return -(value - mu)**2 with pm.Model(): mu = pm.Normal('mu',0,1) pm.DensityDist( 'density_dist', mu, logp=logp, observed=np.random.randn(100), ) idata = pm.sample(100) .. code-block:: python def logp(value, mu): return -(value - mu)**2 def random(mu, rng=None, size=None): return rng.normal(loc=mu, scale=1, size=size) with pm.Model(): mu = pm.Normal('mu', 0 , 1) dens = pm.DensityDist( 'density_dist', mu, logp=logp, random=random, observed=np.random.randn(100, 3), size=(100, 3), ) prior = pm.sample_prior_predictive(10).prior_predictive['density_dist'] assert prior.shape == (1, 10, 100, 3) """ rv_type = DensityDistRV def __new__(cls, name, *args, **kwargs): kwargs.setdefault("class_name", name) return super().__new__(cls, name, *args, **kwargs)
[docs] @classmethod def dist( cls, *dist_params, class_name: str, logp: Optional[Callable] = None, logcdf: Optional[Callable] = None, random: Optional[Callable] = None, moment: Optional[Callable] = None, ndim_supp: int = 0, ndims_params: Optional[Sequence[int]] = None, dtype: str = "floatX", **kwargs, ): if dist_params is None: dist_params = [] elif len(dist_params) > 0 and callable(dist_params[0]): raise TypeError( "The DensityDist API has changed, you are using the old API " "where logp was the first positional argument. In the current API, " "the logp is a keyword argument, amongst other changes. Please refer " "to the API documentation for more information on how to use the " "new DensityDist API." ) dist_params = [as_tensor_variable(param) for param in dist_params] # Assume scalar ndims_params if ndims_params is None: ndims_params = [0] * len(dist_params) if logp is None: logp = default_not_implemented(class_name, "logp") if logcdf is None: logcdf = default_not_implemented(class_name, "logcdf") if moment is None: moment = functools.partial( default_moment, rv_name=class_name, has_fallback=random is not None, ndim_supp=ndim_supp, ) if random is None: random = default_not_implemented(class_name, "random") return super().dist( dist_params, class_name=class_name, logp=logp, logcdf=logcdf, random=random, moment=moment, ndim_supp=ndim_supp, ndims_params=ndims_params, dtype=dtype, **kwargs, )
[docs] @classmethod def rv_op( cls, *dist_params, class_name: str, logp: Optional[Callable], logcdf: Optional[Callable], random: Optional[Callable], moment: Optional[Callable], ndim_supp: int, ndims_params: Optional[Sequence[int]], dtype: str, **kwargs, ): rv_op = type( f"DensityDist_{class_name}", (DensityDistRV,), dict( name=f"DensityDist_{class_name}", inplace=False, ndim_supp=ndim_supp, ndims_params=ndims_params, dtype=dtype, # Specifc to DensityDist _random_fn=random, ), )() # Register custom logp rv_type = type(rv_op) @_logprob.register(rv_type) def density_dist_logp(op, value_var_list, *dist_params, **kwargs): _dist_params = dist_params[3:] value_var = value_var_list[0] return logp(value_var, *_dist_params) @_logcdf.register(rv_type) def density_dist_logcdf(op, var, rvs_to_values, *dist_params, **kwargs): value_var = rvs_to_values.get(var, var) return logcdf(value_var, *dist_params, **kwargs) @_moment.register(rv_type) def density_dist_get_moment(op, rv, rng, size, dtype, *dist_params): return moment(rv, size, *dist_params) return rv_op(*dist_params, **kwargs)
def default_not_implemented(rv_name, method_name): message = ( f"Attempted to run {method_name} on the DensityDist '{rv_name}', " f"but this method had not been provided when the distribution was " f"constructed. Please re-build your model and provide a callable " f"to '{rv_name}'s {method_name} keyword argument.\n" ) def func(*args, **kwargs): raise NotImplementedError(message) return func def default_moment(rv, size, *rv_inputs, rv_name=None, has_fallback=False, ndim_supp=0): if ndim_supp == 0: return at.zeros(size, dtype=rv.dtype) elif has_fallback: return at.zeros_like(rv) else: raise TypeError( "Cannot safely infer the size of a multivariate random variable's moment. " f"Please provide a moment function when instantiating the {rv_name} " "random variable." )