Source code for pymc.variational.opvi

#   Copyright 2020 The PyMC Developers
#
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#   limitations under the License.

R"""
Variational inference is a great approach for doing really complex,
often intractable Bayesian inference in approximate form. Common methods
(e.g. ADVI) lack from complexity so that approximate posterior does not
reveal the true nature of underlying problem. In some applications it can
yield unreliable decisions.

Recently on NIPS 2017 `OPVI  <https://arxiv.org/abs/1610.09033/>`_ framework
was presented. It generalizes variational inference so that the problem is
build with blocks. The first and essential block is Model itself. Second is
Approximation, in some cases :math:`log Q(D)` is not really needed. Necessity
depends on the third and fourth part of that black box, Operator and
Test Function respectively.

Operator is like an approach we use, it constructs loss from given Model,
Approximation and Test Function. The last one is not needed if we minimize
KL Divergence from Q to posterior. As a drawback we need to compute :math:`loq Q(D)`.
Sometimes approximation family is intractable and :math:`loq Q(D)` is not available,
here comes LS(Langevin Stein) Operator with a set of test functions.

Test Function has more unintuitive meaning. It is usually used with LS operator
and represents all we want from our approximate distribution. For any given vector
based function of :math:`z` LS operator yields zero mean function under posterior.
:math:`loq Q(D)` is no more needed. That opens a door to rich approximation
families as neural networks.

References
----------
-   Rajesh Ranganath, Jaan Altosaar, Dustin Tran, David M. Blei
    Operator Variational Inference
    https://arxiv.org/abs/1610.09033 (2016)
"""

from __future__ import annotations

import collections
import itertools
import warnings

import numpy as np
import pytensor
import pytensor.tensor as at

from pytensor.graph.basic import Variable

import pymc as pm

from pymc.backends.base import MultiTrace
from pymc.backends.ndarray import NDArray
from pymc.blocking import DictToArrayBijection
from pymc.distributions.logprob import _get_scaling
from pymc.initial_point import make_initial_point_fn
from pymc.model import modelcontext
from pymc.pytensorf import (
    SeedSequenceSeed,
    at_rng,
    compile_pymc,
    find_rng_nodes,
    identity,
    reseed_rngs,
)
from pymc.util import (
    RandomState,
    WithMemoization,
    _get_seeds_per_chain,
    locally_cachedmethod,
)
from pymc.variational.updates import adagrad_window
from pymc.vartypes import discrete_types

__all__ = ["ObjectiveFunction", "Operator", "TestFunction", "Group", "Approximation"]


class VariationalInferenceError(Exception):
    """Exception for VI specific cases"""


class NotImplementedInference(VariationalInferenceError, NotImplementedError):
    """Marking non functional parts of code"""


class ExplicitInferenceError(VariationalInferenceError, TypeError):
    """Exception for bad explicit inference"""


class AEVBInferenceError(VariationalInferenceError, TypeError):
    """Exception for bad aevb inference"""


class ParametrizationError(VariationalInferenceError, ValueError):
    """Error raised in case of bad parametrization"""


class GroupError(VariationalInferenceError, TypeError):
    """Error related to VI groups"""


def append_name(name):
    def wrap(f):
        if name is None:
            return f

        def inner(*args, **kwargs):
            res = f(*args, **kwargs)
            res.name = name
            return res

        return inner

    return wrap


def node_property(f):
    """A shortcut for wrapping method to accessible tensor"""

    if isinstance(f, str):

        def wrapper(fn):
            ff = append_name(f)(fn)
            f_ = pytensor.config.change_flags(compute_test_value="off")(ff)
            return property(locally_cachedmethod(f_))

        return wrapper
    else:
        f_ = pytensor.config.change_flags(compute_test_value="off")(f)
        return property(locally_cachedmethod(f_))


@pytensor.config.change_flags(compute_test_value="ignore")
def try_to_set_test_value(node_in, node_out, s):
    _s = s
    if s is None:
        s = 1
    s = pytensor.compile.view_op(at.as_tensor(s))
    if not isinstance(node_in, (list, tuple)):
        node_in = [node_in]
    if not isinstance(node_out, (list, tuple)):
        node_out = [node_out]
    for i, o in zip(node_in, node_out):
        if hasattr(i.tag, "test_value"):
            if not hasattr(s.tag, "test_value"):
                continue
            else:
                tv = i.tag.test_value[None, ...]
                tv = np.repeat(tv, s.tag.test_value, 0)
                if _s is None:
                    tv = tv[0]
                o.tag.test_value = tv


class ObjectiveUpdates(pytensor.OrderedUpdates):
    """OrderedUpdates extension for storing loss"""

    loss = None


def _warn_not_used(smth, where):
    warnings.warn(f"`{smth}` is not used for {where} and ignored")


class ObjectiveFunction:
    """Helper class for construction loss and updates for variational inference

    Parameters
    ----------
    op : :class:`Operator`
        OPVI Functional operator
    tf : :class:`TestFunction`
        OPVI TestFunction
    """

    def __init__(self, op: Operator, tf: TestFunction):
        self.op = op
        self.tf = tf

    obj_params = property(lambda self: self.op.approx.params)
    test_params = property(lambda self: self.tf.params)
    approx = property(lambda self: self.op.approx)

    def updates(
        self,
        obj_n_mc=None,
        tf_n_mc=None,
        obj_optimizer=adagrad_window,
        test_optimizer=adagrad_window,
        more_obj_params=None,
        more_tf_params=None,
        more_updates=None,
        more_replacements=None,
        total_grad_norm_constraint=None,
    ):
        """Calculate gradients for objective function, test function and then
        constructs updates for optimization step

        Parameters
        ----------
        obj_n_mc : int
            Number of monte carlo samples used for approximation of objective gradients
        tf_n_mc : int
            Number of monte carlo samples used for approximation of test function gradients
        obj_optimizer : function (loss, params) -> updates
            Optimizer that is used for objective params
        test_optimizer : function (loss, params) -> updates
            Optimizer that is used for test function params
        more_obj_params : list
            Add custom params for objective optimizer
        more_tf_params : list
            Add custom params for test function optimizer
        more_updates : dict
            Add custom updates to resulting updates
        more_replacements : dict
            Apply custom replacements before calculating gradients
        total_grad_norm_constraint : float
            Bounds gradient norm, prevents exploding gradient problem

        Returns
        -------
        :class:`ObjectiveUpdates`
        """
        if more_updates is None:
            more_updates = dict()
        resulting_updates = ObjectiveUpdates()
        if self.test_params:
            self.add_test_updates(
                resulting_updates,
                tf_n_mc=tf_n_mc,
                test_optimizer=test_optimizer,
                more_tf_params=more_tf_params,
                more_replacements=more_replacements,
                total_grad_norm_constraint=total_grad_norm_constraint,
            )
        else:
            if tf_n_mc is not None:
                _warn_not_used("tf_n_mc", self.op)
            if more_tf_params:
                _warn_not_used("more_tf_params", self.op)
        self.add_obj_updates(
            resulting_updates,
            obj_n_mc=obj_n_mc,
            obj_optimizer=obj_optimizer,
            more_obj_params=more_obj_params,
            more_replacements=more_replacements,
            total_grad_norm_constraint=total_grad_norm_constraint,
        )
        resulting_updates.update(more_updates)
        return resulting_updates

    def add_test_updates(
        self,
        updates,
        tf_n_mc=None,
        test_optimizer=adagrad_window,
        more_tf_params=None,
        more_replacements=None,
        total_grad_norm_constraint=None,
    ):
        if more_tf_params is None:
            more_tf_params = []
        if more_replacements is None:
            more_replacements = dict()
        tf_target = self(
            tf_n_mc, more_tf_params=more_tf_params, more_replacements=more_replacements
        )
        grads = pm.updates.get_or_compute_grads(tf_target, self.obj_params + more_tf_params)
        if total_grad_norm_constraint is not None:
            grads = pm.total_norm_constraint(grads, total_grad_norm_constraint)
        updates.update(test_optimizer(grads, self.test_params + more_tf_params))

    def add_obj_updates(
        self,
        updates,
        obj_n_mc=None,
        obj_optimizer=adagrad_window,
        more_obj_params=None,
        more_replacements=None,
        total_grad_norm_constraint=None,
    ):
        if more_obj_params is None:
            more_obj_params = []
        if more_replacements is None:
            more_replacements = dict()
        obj_target = self(
            obj_n_mc, more_obj_params=more_obj_params, more_replacements=more_replacements
        )
        grads = pm.updates.get_or_compute_grads(obj_target, self.obj_params + more_obj_params)
        if total_grad_norm_constraint is not None:
            grads = pm.total_norm_constraint(grads, total_grad_norm_constraint)
        updates.update(obj_optimizer(grads, self.obj_params + more_obj_params))
        if self.op.returns_loss:
            updates.loss = obj_target

    @pytensor.config.change_flags(compute_test_value="off")
    def step_function(
        self,
        obj_n_mc=None,
        tf_n_mc=None,
        obj_optimizer=adagrad_window,
        test_optimizer=adagrad_window,
        more_obj_params=None,
        more_tf_params=None,
        more_updates=None,
        more_replacements=None,
        total_grad_norm_constraint=None,
        score=False,
        fn_kwargs=None,
    ):
        R"""Step function that should be called on each optimization step.

        Generally it solves the following problem:

        .. math::

                \mathbf{\lambda^{\*}} = \inf_{\lambda} \sup_{\theta} t(\mathbb{E}_{\lambda}[(O^{p,q}f_{\theta})(z)])

        Parameters
        ----------
        obj_n_mc: `int`
            Number of monte carlo samples used for approximation of objective gradients
        tf_n_mc: `int`
            Number of monte carlo samples used for approximation of test function gradients
        obj_optimizer: function (grads, params) -> updates
            Optimizer that is used for objective params
        test_optimizer: function (grads, params) -> updates
            Optimizer that is used for test function params
        more_obj_params: `list`
            Add custom params for objective optimizer
        more_tf_params: `list`
            Add custom params for test function optimizer
        more_updates: `dict`
            Add custom updates to resulting updates
        total_grad_norm_constraint: `float`
            Bounds gradient norm, prevents exploding gradient problem
        score: `bool`
            calculate loss on each step? Defaults to False for speed
        fn_kwargs: `dict`
            Add kwargs to pytensor.function (e.g. `{'profile': True}`)
        more_replacements: `dict`
            Apply custom replacements before calculating gradients

        Returns
        -------
        `pytensor.function`
        """
        if fn_kwargs is None:
            fn_kwargs = {}
        if score and not self.op.returns_loss:
            raise NotImplementedError("%s does not have loss" % self.op)
        updates = self.updates(
            obj_n_mc=obj_n_mc,
            tf_n_mc=tf_n_mc,
            obj_optimizer=obj_optimizer,
            test_optimizer=test_optimizer,
            more_obj_params=more_obj_params,
            more_tf_params=more_tf_params,
            more_updates=more_updates,
            more_replacements=more_replacements,
            total_grad_norm_constraint=total_grad_norm_constraint,
        )
        if score:
            step_fn = compile_pymc([], updates.loss, updates=updates, **fn_kwargs)
        else:
            step_fn = compile_pymc([], [], updates=updates, **fn_kwargs)
        return step_fn

    @pytensor.config.change_flags(compute_test_value="off")
    def score_function(
        self, sc_n_mc=None, more_replacements=None, fn_kwargs=None
    ):  # pragma: no cover
        R"""Compile scoring function that operates which takes no inputs and returns Loss

        Parameters
        ----------
        sc_n_mc: `int`
            number of scoring MC samples
        more_replacements:
            Apply custom replacements before compiling a function
        fn_kwargs: `dict`
            arbitrary kwargs passed to `pytensor.function`

        Returns
        -------
        pytensor.function
        """
        if fn_kwargs is None:
            fn_kwargs = {}
        if not self.op.returns_loss:
            raise NotImplementedError("%s does not have loss" % self.op)
        if more_replacements is None:
            more_replacements = {}
        loss = self(sc_n_mc, more_replacements=more_replacements)
        return compile_pymc([], loss, **fn_kwargs)

    @pytensor.config.change_flags(compute_test_value="off")
    def __call__(self, nmc, **kwargs):
        if "more_tf_params" in kwargs:
            m = -1.0
        else:
            m = 1.0
        a = self.op.apply(self.tf)
        a = self.approx.set_size_and_deterministic(a, nmc, 0, kwargs.get("more_replacements"))
        return m * self.op.T(a)


class Operator:
    R"""**Base class for Operator**

    Parameters
    ----------
    approx: :class:`Approximation`
        an approximation instance

    Notes
    -----
    For implementing custom operator it is needed to define :func:`Operator.apply` method
    """

    has_test_function = False
    returns_loss = True
    require_logq = True
    objective_class = ObjectiveFunction
    supports_aevb = property(lambda self: not self.approx.any_histograms)
    T = identity

    def __init__(self, approx):
        self.approx = approx
        if self.require_logq and not approx.has_logq:
            raise ExplicitInferenceError(
                "%s requires logq, but %s does not implement it"
                "please change inference method" % (self, approx)
            )

    inputs = property(lambda self: self.approx.inputs)
    logp = property(lambda self: self.approx.logp)
    varlogp = property(lambda self: self.approx.varlogp)
    datalogp = property(lambda self: self.approx.datalogp)
    logq = property(lambda self: self.approx.logq)
    logp_norm = property(lambda self: self.approx.logp_norm)
    varlogp_norm = property(lambda self: self.approx.varlogp_norm)
    datalogp_norm = property(lambda self: self.approx.datalogp_norm)
    logq_norm = property(lambda self: self.approx.logq_norm)
    model = property(lambda self: self.approx.model)

    def apply(self, f):  # pragma: no cover
        R"""Operator itself

        .. math::

            (O^{p,q}f_{\theta})(z)

        Parameters
        ----------
        f: :class:`TestFunction` or None
            function that takes `z = self.input` and returns
            same dimensional output

        Returns
        -------
        TensorVariable
            symbolically applied operator
        """
        raise NotImplementedError

    def __call__(self, f=None):
        if self.has_test_function:
            if f is None:
                raise ParametrizationError("Operator %s requires TestFunction" % self)
            else:
                if not isinstance(f, TestFunction):
                    f = TestFunction.from_function(f)
        else:
            if f is not None:
                warnings.warn("TestFunction for %s is redundant and removed" % self, stacklevel=3)
            else:
                pass
            f = TestFunction()
        f.setup(self.approx)
        return self.objective_class(self, f)

    def __str__(self):  # pragma: no cover
        return "%(op)s[%(ap)s]" % dict(
            op=self.__class__.__name__, ap=self.approx.__class__.__name__
        )


def collect_shared_to_list(params):
    """Helper function for getting a list from
    usable representation of parameters

    Parameters
    ----------
    params: {dict|None}

    Returns
    -------
    List
    """
    if isinstance(params, dict):
        return list(
            t[1]
            for t in sorted(params.items(), key=lambda t: t[0])
            if isinstance(t[1], pytensor.compile.SharedVariable)
        )
    elif params is None:
        return []
    else:
        raise TypeError("Unknown type %s for %r, need dict or None")


class TestFunction:
    def __init__(self):
        self._inited = False
        self.shared_params = None

    @property
    def params(self):
        return collect_shared_to_list(self.shared_params)

    def __call__(self, z):
        raise NotImplementedError

    def setup(self, approx):
        pass

    @classmethod
    def from_function(cls, f):
        if not callable(f):
            raise ParametrizationError("Need callable, got %r" % f)
        obj = TestFunction()
        obj.__call__ = f
        return obj


[docs]class Group(WithMemoization): R"""**Base class for grouping variables in VI** Grouped Approximation is used for modelling mutual dependencies for a specified group of variables. Base for local and global group. Parameters ---------- group: list List of PyMC variables or None indicating that group takes all the rest variables vfam: str String that marks the corresponding variational family for the group. Cannot be passed both with `params` params: dict Dict with variational family parameters, full description can be found below. Cannot be passed both with `vfam` random_seed: int Random seed for underlying random generator model : PyMC Model options: dict Special options for the group kwargs: Other kwargs for the group Notes ----- Group instance/class has some important constants: - **has_logq** Tells that distribution is defined explicitly These constants help providing the correct inference method for given parametrization Examples -------- **Basic Initialization** :class:`Group` is a factory class. You do not need to call every ApproximationGroup explicitly. Passing the correct `vfam` (Variational FAMily) argument you'll tell what parametrization is desired for the group. This helps not to overload code with lots of classes. .. code:: python >>> group = Group([latent1, latent2], vfam='mean_field') The other way to select approximation is to provide `params` dictionary that has some predefined well shaped parameters. Keys of the dict serve as an identifier for variational family and help to autoselect the correct group class. To identify what approximation to use, params dict should have the full set of needed parameters. As there are 2 ways to instantiate the :class:`Group` passing both `vfam` and `params` is prohibited. Partial parametrization is prohibited by design to avoid corner cases and possible problems. .. code:: python >>> group = Group([latent3], params=dict(mu=my_mu, rho=my_rho)) Important to note that in case you pass custom params they will not be autocollected by optimizer, you'll have to provide them with `more_obj_params` keyword. **Supported dict keys:** - `{'mu', 'rho'}`: :class:`MeanFieldGroup` - `{'mu', 'L_tril'}`: :class:`FullRankGroup` - `{'histogram'}`: :class:`EmpiricalGroup` **Delayed Initialization** When you have a lot of latent variables it is impractical to do it all manually. To make life much simpler, You can pass `None` instead of list of variables. That case you'll not create shared parameters until you pass all collected groups to Approximation object that collects all the groups together and checks that every group is correctly initialized. For those groups which have group equal to `None` it will collect all the rest variables not covered by other groups and perform delayed init. .. code:: python >>> group_1 = Group([latent1], vfam='fr') # latent1 has full rank approximation >>> group_other = Group(None, vfam='mf') # other variables have mean field Q >>> approx = Approximation([group_1, group_other]) **Summing Up** When you have created all the groups they need to pass all the groups to :class:`Approximation`. It does not accept any other parameter rather than `groups` .. code:: python >>> approx = Approximation(my_groups) See Also -------- :class:`Approximation` References ---------- - Kingma, D. P., & Welling, M. (2014). `Auto-Encoding Variational Bayes. stat, 1050, 1. <https://arxiv.org/abs/1312.6114>`_ """ # needs to be defined in init shared_params = None symbolic_initial = None replacements = None input = None # defined by approximation has_logq = True # some important defaults initial_dist_name = "normal" initial_dist_map = 0.0 # for handy access using class methods __param_spec__ = dict() short_name = "" alias_names = frozenset() __param_registry = dict() __name_registry = dict()
[docs] @classmethod def register(cls, sbcls): assert ( frozenset(sbcls.__param_spec__) not in cls.__param_registry ), "Duplicate __param_spec__" cls.__param_registry[frozenset(sbcls.__param_spec__)] = sbcls assert sbcls.short_name not in cls.__name_registry, "Duplicate short_name" cls.__name_registry[sbcls.short_name] = sbcls for alias in sbcls.alias_names: assert alias not in cls.__name_registry, "Duplicate alias_name" cls.__name_registry[alias] = sbcls return sbcls
[docs] @classmethod def group_for_params(cls, params): if frozenset(params) not in cls.__param_registry: raise KeyError( "No such group for the following params: {!r}, " "only the following are supported\n\n{}".format(params, cls.__param_registry) ) return cls.__param_registry[frozenset(params)]
[docs] @classmethod def group_for_short_name(cls, name): if name.lower() not in cls.__name_registry: raise KeyError( "No such group: {!r}, " "only the following are supported\n\n{}".format(name, cls.__name_registry) ) return cls.__name_registry[name.lower()]
def __new__(cls, group=None, vfam=None, params=None, *args, **kwargs): if cls is Group: if vfam is not None and params is not None: raise TypeError("Cannot call Group with both `vfam` and `params` provided") elif vfam is not None: return super().__new__(cls.group_for_short_name(vfam)) elif params is not None: return super().__new__(cls.group_for_params(params)) else: raise TypeError("Need to call Group with either `vfam` or `params` provided") else: return super().__new__(cls)
[docs] def __init__( self, group, vfam=None, params=None, random_seed=None, model=None, options=None, **kwargs, ): if isinstance(vfam, str): vfam = vfam.lower() if options is None: options = dict() self.options = options self._vfam = vfam self.rng = np.random.default_rng(random_seed) self._rng = at_rng(random_seed) model = modelcontext(model) self.model = model self.group = group self.user_params = params self._user_params = None self.replacements = collections.OrderedDict() self.ordering = collections.OrderedDict() # save this stuff to use in __init_group__ later self._kwargs = kwargs if self.group is not None: # init can be delayed self.__init_group__(self.group)
def _prepare_start(self, start=None): ipfn = make_initial_point_fn( model=self.model, overrides=start, jitter_rvs={}, return_transformed=True, ) start = ipfn(self.rng.integers(2**30, dtype=np.int64)) group_vars = {self.model.rvs_to_values[v].name for v in self.group} start = {k: v for k, v in start.items() if k in group_vars} start = DictToArrayBijection.map(start).data return start
[docs] @classmethod def get_param_spec_for(cls, **kwargs): res = dict() for name, fshape in cls.__param_spec__.items(): res[name] = tuple(eval(s, kwargs) for s in fshape) return res
def _check_user_params(self, **kwargs): R"""*Dev* - checks user params, allocates them if they are correct, returns True. If they are not present, returns False Parameters ---------- kwargs: special kwargs needed sometimes Returns ------- bool indicating whether to allocate new shared params """ user_params = self.user_params if user_params is None: return False if not isinstance(user_params, dict): raise TypeError("params should be a dict") givens = set(user_params.keys()) needed = set(self.__param_spec__) if givens != needed: raise ParametrizationError( "Passed parameters do not have a needed set of keys, " "they should be equal, got {givens}, needed {needed}".format( givens=givens, needed=needed ) ) self._user_params = dict() spec = self.get_param_spec_for(d=self.ddim, **kwargs.pop("spec_kw", {})) for name, param in self.user_params.items(): shape = spec[name] self._user_params[name] = at.as_tensor(param).reshape(shape) return True def _initial_type(self, name): R"""*Dev* - initial type with given name. The correct type depends on `self.batched` Parameters ---------- name: str name for tensor Returns ------- tensor """ return at.matrix(name) def _input_type(self, name): R"""*Dev* - input type with given name. The correct type depends on `self.batched` Parameters ---------- name: str name for tensor Returns ------- tensor """ return at.vector(name) @pytensor.config.change_flags(compute_test_value="off") def __init_group__(self, group): if not group: raise GroupError("Got empty group") if self.group is None: # delayed init self.group = group self.symbolic_initial = self._initial_type( self.__class__.__name__ + "_symbolic_initial_tensor" ) self.input = self._input_type(self.__class__.__name__ + "_symbolic_input") # I do some staff that is not supported by standard __init__ # so I have to to it by myself # 1) we need initial point (transformed space) model_initial_point = self.model.initial_point(0) # 2) we'll work with a single group, a subset of the model # here we need to create a mapping to replace value_vars with slices from the approximation start_idx = 0 for var in self.group: if var.type.numpy_dtype.name in discrete_types: raise ParametrizationError(f"Discrete variables are not supported by VI: {var}") # 3) This is the way to infer shape and dtype of the variable value_var = self.model.rvs_to_values[var] test_var = model_initial_point[value_var.name] shape = test_var.shape size = test_var.size dtype = test_var.dtype vr = self.input[..., start_idx : start_idx + size].reshape(shape).astype(dtype) vr.name = value_var.name + "_vi_replacement" self.replacements[value_var] = vr self.ordering[value_var.name] = ( value_var.name, slice(start_idx, start_idx + size), shape, dtype, ) start_idx += size def _finalize_init(self): """*Dev* - clean up after init""" del self._kwargs @property def params_dict(self): # prefixed are correctly reshaped if self._user_params is not None: return self._user_params else: return self.shared_params @property def params(self): # raw user params possibly not reshaped if self.user_params is not None: return collect_shared_to_list(self.user_params) else: return collect_shared_to_list(self.shared_params) def _new_initial_shape(self, size, dim, more_replacements=None): """*Dev* - correctly proceeds sampling with variable batch size Parameters ---------- size: scalar sample size dim: scalar latent fixed dim more_replacements: dict replacements for latent batch shape Returns ------- shape vector """ return at.stack([size, dim]) @node_property def ndim(self): return self.ddim @property def ddim(self): return sum(s.stop - s.start for _, s, _, _ in self.ordering.values()) def _new_initial(self, size, deterministic, more_replacements=None): """*Dev* - allocates new initial random generator Parameters ---------- size: scalar sample size deterministic: bool or scalar whether to sample in deterministic manner more_replacements: dict more replacements passed to shape Notes ----- Suppose you have a AEVB setup that: - input `X` is purely symbolic, and `X.shape[0]` is needed to `initial` second dim - to perform inference, `X` is replaced with data tensor, however, since `X.shape[0]` in `initial` remains symbolic and can't be replaced, you get `MissingInputError` - as a solution, here we perform a manual replacement for the second dim in `initial`. Returns ------- tensor """ if size is None: size = 1 if not isinstance(deterministic, Variable): deterministic = np.int8(deterministic) dim, dist_name, dist_map = (self.ddim, self.initial_dist_name, self.initial_dist_map) dtype = self.symbolic_initial.dtype dim = at.as_tensor(dim) size = at.as_tensor(size) shape = self._new_initial_shape(size, dim, more_replacements) # apply optimizations if possible if not isinstance(deterministic, Variable): if deterministic: return at.ones(shape, dtype) * dist_map else: return getattr(self._rng, dist_name)(size=shape) else: sample = getattr(self._rng, dist_name)(size=shape) initial = at.switch(deterministic, at.ones(shape, dtype) * dist_map, sample) return initial @node_property def symbolic_random(self): """*Dev* - abstract node that takes `self.symbolic_initial` and creates approximate posterior that is parametrized with `self.params_dict`. Implementation should take in account `self.batched`. If `self.batched` is `True`, then `self.symbolic_initial` is 3d tensor, else 2d Returns ------- tensor """ raise NotImplementedError
[docs] @pytensor.config.change_flags(compute_test_value="off") def set_size_and_deterministic( self, node: Variable, s, d: bool, more_replacements: dict | None = None ) -> list[Variable]: """*Dev* - after node is sampled via :func:`symbolic_sample_over_posterior` or :func:`symbolic_single_sample` new random generator can be allocated and applied to node Parameters ---------- node: :class:`Variable` PyTensor node with symbolically applied VI replacements s: scalar desired number of samples d: bool or int whether sampling is done deterministically more_replacements: dict more replacements to apply Returns ------- :class:`Variable` with applied replacements, ready to use """ flat2rand = self.make_size_and_deterministic_replacements(s, d, more_replacements) node_out = pytensor.clone_replace(node, flat2rand) try_to_set_test_value(node, node_out, s) return node_out
[docs] def to_flat_input(self, node): """*Dev* - replace vars with flattened view stored in `self.inputs`""" return pytensor.clone_replace(node, self.replacements)
[docs] def symbolic_sample_over_posterior(self, node): """*Dev* - performs sampling of node applying independent samples from posterior each time. Note that it is done symbolically and this node needs :func:`set_size_and_deterministic` call """ node = self.to_flat_input(node) random = self.symbolic_random.astype(self.symbolic_initial.dtype) random = at.specify_shape(random, self.symbolic_initial.type.shape) def sample(post, node): return pytensor.clone_replace(node, {self.input: post}) nodes, _ = pytensor.scan(sample, random, non_sequences=[node]) return nodes
[docs] def symbolic_single_sample(self, node): """*Dev* - performs sampling of node applying single sample from posterior. Note that it is done symbolically and this node needs :func:`set_size_and_deterministic` call with `size=1` """ node = self.to_flat_input(node) random = self.symbolic_random.astype(self.symbolic_initial.dtype) return pytensor.clone_replace(node, {self.input: random[0]})
[docs] def make_size_and_deterministic_replacements(self, s, d, more_replacements=None): """*Dev* - creates correct replacements for initial depending on sample size and deterministic flag Parameters ---------- s: scalar sample size d: bool or scalar whether sampling is done deterministically more_replacements: dict replacements for shape and initial Returns ------- dict with replacements for initial """ initial = self._new_initial(s, d, more_replacements) initial = at.specify_shape(initial, self.symbolic_initial.type.shape) if more_replacements: initial = pytensor.clone_replace(initial, more_replacements) return {self.symbolic_initial: initial}
@node_property def symbolic_normalizing_constant(self): """*Dev* - normalizing constant for `self.logq`, scales it to `minibatch_size` instead of `total_size`""" t = self.to_flat_input( at.max( [ _get_scaling(self.model.rvs_to_total_sizes.get(v, None), v.shape, v.ndim) for v in self.group ] ) ) t = self.symbolic_single_sample(t) return pm.floatX(t) @node_property def symbolic_logq_not_scaled(self): """*Dev* - symbolically computed logq for `self.symbolic_random` computations can be more efficient since all is known beforehand including `self.symbolic_random` """ raise NotImplementedError # shape (s,) @node_property def symbolic_logq(self): """*Dev* - correctly scaled `self.symbolic_logq_not_scaled`""" return self.symbolic_logq_not_scaled @node_property def logq(self): """*Dev* - Monte Carlo estimate for group `logQ`""" return self.symbolic_logq.mean(0) @node_property def logq_norm(self): """*Dev* - Monte Carlo estimate for group `logQ` normalized""" return self.logq / self.symbolic_normalizing_constant def __str__(self): if self.group is None: shp = "undefined" else: shp = str(self.ddim) return f"{self.__class__.__name__}[{shp}]" @node_property def std(self): raise NotImplementedError @node_property def cov(self): raise NotImplementedError @node_property def mean(self): raise NotImplementedError
group_for_params = Group.group_for_params group_for_short_name = Group.group_for_short_name
[docs]class Approximation(WithMemoization): """**Wrapper for grouped approximations** Wraps list of groups, creates an Approximation instance that collects sampled variables from all the groups, also collects logQ needed for explicit Variational Inference. Parameters ---------- groups: list[Group] List of :class:`Group` instances. They should have all model variables model: Model Notes ----- Some shortcuts for single group approximations are available: - :class:`MeanField` - :class:`FullRank` - :class:`Empirical` See Also -------- :class:`Group` """
[docs] def __init__(self, groups, model=None): self._scale_cost_to_minibatch = pytensor.shared(np.int8(1)) model = modelcontext(model) if not model.free_RVs: raise TypeError("Model does not have an free RVs") self.groups = list() seen = set() rest = None for g in groups: if g.group is None: if rest is not None: raise GroupError("More than one group is specified for " "the rest variables") else: rest = g else: if set(g.group) & seen: raise GroupError("Found duplicates in groups") seen.update(g.group) self.groups.append(g) # List iteration to preserve order for reproducibility between runs unseen_free_RVs = [var for var in model.free_RVs if var not in seen] if unseen_free_RVs: if rest is None: raise GroupError("No approximation is specified for the rest variables") else: rest.__init_group__(unseen_free_RVs) self.groups.append(rest) self.model = model
@property def has_logq(self): return all(self.collect("has_logq"))
[docs] def collect(self, item): return [getattr(g, item) for g in self.groups]
inputs = property(lambda self: self.collect("input")) symbolic_randoms = property(lambda self: self.collect("symbolic_random")) @property def scale_cost_to_minibatch(self): """*Dev* - Property to control scaling cost to minibatch""" return bool(self._scale_cost_to_minibatch.get_value()) @scale_cost_to_minibatch.setter def scale_cost_to_minibatch(self, value): self._scale_cost_to_minibatch.set_value(np.int8(bool(value))) @node_property def symbolic_normalizing_constant(self): """*Dev* - normalizing constant for `self.logq`, scales it to `minibatch_size` instead of `total_size`. Here the effect is controlled by `self.scale_cost_to_minibatch` """ t = at.max( self.collect("symbolic_normalizing_constant") + [ _get_scaling( self.model.rvs_to_total_sizes.get(obs, None), obs.shape, obs.ndim, ) for obs in self.model.observed_RVs ] ) t = at.switch(self._scale_cost_to_minibatch, t, at.constant(1, dtype=t.dtype)) return pm.floatX(t) @node_property def symbolic_logq(self): """*Dev* - collects `symbolic_logq` for all groups""" return at.add(*self.collect("symbolic_logq")) @node_property def logq(self): """*Dev* - collects `logQ` for all groups""" return at.add(*self.collect("logq")) @node_property def logq_norm(self): """*Dev* - collects `logQ` for all groups and normalizes it""" return self.logq / self.symbolic_normalizing_constant @node_property def _sized_symbolic_varlogp_and_datalogp(self): """*Dev* - computes sampled prior term from model via `pytensor.scan`""" varlogp_s, datalogp_s = self.symbolic_sample_over_posterior( [self.model.varlogp, self.model.datalogp] ) return varlogp_s, datalogp_s # both shape (s,) @node_property def sized_symbolic_varlogp(self): """*Dev* - computes sampled prior term from model via `pytensor.scan`""" return self._sized_symbolic_varlogp_and_datalogp[0] # shape (s,) @node_property def sized_symbolic_datalogp(self): """*Dev* - computes sampled data term from model via `pytensor.scan`""" return self._sized_symbolic_varlogp_and_datalogp[1] # shape (s,) @node_property def sized_symbolic_logp(self): """*Dev* - computes sampled logP from model via `pytensor.scan`""" return self.sized_symbolic_varlogp + self.sized_symbolic_datalogp # shape (s,) @node_property def logp(self): """*Dev* - computes :math:`E_{q}(logP)` from model via `pytensor.scan` that can be optimized later""" return self.varlogp + self.datalogp @node_property def varlogp(self): """*Dev* - computes :math:`E_{q}(prior term)` from model via `pytensor.scan` that can be optimized later""" return self.sized_symbolic_varlogp.mean(0) @node_property def datalogp(self): """*Dev* - computes :math:`E_{q}(data term)` from model via `pytensor.scan` that can be optimized later""" return self.sized_symbolic_datalogp.mean(0) @node_property def _single_symbolic_varlogp_and_datalogp(self): """*Dev* - computes sampled prior term from model via `pytensor.scan`""" varlogp, datalogp = self.symbolic_single_sample([self.model.varlogp, self.model.datalogp]) return varlogp, datalogp @node_property def single_symbolic_varlogp(self): """*Dev* - for single MC sample estimate of :math:`E_{q}(prior term)` `pytensor.scan` is not needed and code can be optimized""" return self._single_symbolic_varlogp_and_datalogp[0] @node_property def single_symbolic_datalogp(self): """*Dev* - for single MC sample estimate of :math:`E_{q}(data term)` `pytensor.scan` is not needed and code can be optimized""" return self._single_symbolic_varlogp_and_datalogp[1] @node_property def single_symbolic_logp(self): """*Dev* - for single MC sample estimate of :math:`E_{q}(logP)` `pytensor.scan` is not needed and code can be optimized""" return self.single_symbolic_datalogp + self.single_symbolic_varlogp @node_property def logp_norm(self): """*Dev* - normalized :math:`E_{q}(logP)`""" return self.logp / self.symbolic_normalizing_constant @node_property def varlogp_norm(self): """*Dev* - normalized :math:`E_{q}(prior term)`""" return self.varlogp / self.symbolic_normalizing_constant @node_property def datalogp_norm(self): """*Dev* - normalized :math:`E_{q}(data term)`""" return self.datalogp / self.symbolic_normalizing_constant @property def replacements(self): """*Dev* - all replacements from groups to replace PyMC random variables with approximation""" return collections.OrderedDict( itertools.chain.from_iterable(g.replacements.items() for g in self.groups) )
[docs] def make_size_and_deterministic_replacements(self, s, d, more_replacements=None): """*Dev* - creates correct replacements for initial depending on sample size and deterministic flag Parameters ---------- s: scalar sample size d: bool whether sampling is done deterministically more_replacements: dict replacements for shape and initial Returns ------- dict with replacements for initial """ if more_replacements is None: more_replacements = {} flat2rand = collections.OrderedDict() for g in self.groups: flat2rand.update(g.make_size_and_deterministic_replacements(s, d, more_replacements)) flat2rand.update(more_replacements) return flat2rand
[docs] @pytensor.config.change_flags(compute_test_value="off") def set_size_and_deterministic(self, node, s, d, more_replacements=None): """*Dev* - after node is sampled via :func:`symbolic_sample_over_posterior` or :func:`symbolic_single_sample` new random generator can be allocated and applied to node Parameters ---------- node: :class:`Variable` PyTensor node with symbolically applied VI replacements s: scalar desired number of samples d: bool or int whether sampling is done deterministically more_replacements: dict more replacements to apply Returns ------- :class:`Variable` with applied replacements, ready to use """ _node = node optimizations = self.get_optimization_replacements(s, d) flat2rand = self.make_size_and_deterministic_replacements(s, d, more_replacements) node = pytensor.clone_replace(node, optimizations) node = pytensor.clone_replace(node, flat2rand) try_to_set_test_value(_node, node, s) return node
[docs] def to_flat_input(self, node, more_replacements=None): """*Dev* - replace vars with flattened view stored in `self.inputs`""" more_replacements = more_replacements or {} node = pytensor.clone_replace(node, more_replacements) return pytensor.clone_replace(node, self.replacements)
[docs] def symbolic_sample_over_posterior(self, node, more_replacements=None): """*Dev* - performs sampling of node applying independent samples from posterior each time. Note that it is done symbolically and this node needs :func:`set_size_and_deterministic` call """ node = self.to_flat_input(node, more_replacements=more_replacements) def sample(*post): return pytensor.clone_replace(node, dict(zip(self.inputs, post))) nodes, _ = pytensor.scan(sample, self.symbolic_randoms) return nodes
[docs] def symbolic_single_sample(self, node, more_replacements=None): """*Dev* - performs sampling of node applying single sample from posterior. Note that it is done symbolically and this node needs :func:`set_size_and_deterministic` call with `size=1` """ node = self.to_flat_input(node, more_replacements=more_replacements) post = [v[0] for v in self.symbolic_randoms] inp = self.inputs return pytensor.clone_replace(node, dict(zip(inp, post)))
[docs] def get_optimization_replacements(self, s, d): """*Dev* - optimizations for logP. If sample size is static and equal to 1: then `pytensor.scan` MC estimate is replaced with single sample without call to `pytensor.scan`. """ repl = collections.OrderedDict() # avoid scan if size is constant and equal to one if isinstance(s, int) and (s == 1) or s is None: repl[self.varlogp] = self.single_symbolic_varlogp repl[self.datalogp] = self.single_symbolic_datalogp return repl
[docs] @pytensor.config.change_flags(compute_test_value="off") def sample_node(self, node, size=None, deterministic=False, more_replacements=None): """Samples given node or nodes over shared posterior Parameters ---------- node: PyTensor Variables (or PyTensor expressions) size: None or scalar number of samples more_replacements: `dict` add custom replacements to graph, e.g. change input source deterministic: bool whether to use zeros as initial distribution if True - zero initial point will produce constant latent variables Returns ------- sampled node(s) with replacements """ node_in = node if more_replacements: node = pytensor.clone_replace(node, more_replacements) if not isinstance(node, (list, tuple)): node = [node] node = self.model.replace_rvs_by_values(node) if not isinstance(node_in, (list, tuple)): node = node[0] if size is None: node_out = self.symbolic_single_sample(node) else: node_out = self.symbolic_sample_over_posterior(node) node_out = self.set_size_and_deterministic(node_out, size, deterministic) try_to_set_test_value(node_in, node_out, size) return node_out
[docs] def rslice(self, name): """*Dev* - vectorized sampling for named random variable without call to `pytensor.scan`. This node still needs :func:`set_size_and_deterministic` to be evaluated """ def vars_names(vs): return {self.model.rvs_to_values[v].name for v in vs} for vars_, random, ordering in zip( self.collect("group"), self.symbolic_randoms, self.collect("ordering") ): if name in vars_names(vars_): name_, slc, shape, dtype = ordering[name] found = random[..., slc].reshape((random.shape[0],) + shape).astype(dtype) found.name = name + "_vi_random_slice" break else: raise KeyError("%r not found" % name) return found
@node_property def sample_dict_fn(self): s = at.iscalar() names = [self.model.rvs_to_values[v].name for v in self.model.free_RVs] sampled = [self.rslice(name) for name in names] sampled = self.set_size_and_deterministic(sampled, s, 0) sample_fn = compile_pymc([s], sampled) rng_nodes = find_rng_nodes(sampled) def inner(draws=100, *, random_seed: SeedSequenceSeed = None): if random_seed is not None: reseed_rngs(rng_nodes, random_seed) _samples = sample_fn(draws) return {v_: s_ for v_, s_ in zip(names, _samples)} return inner
[docs] def sample( self, draws=500, *, random_seed: RandomState = None, return_inferencedata=True, **kwargs ): """Draw samples from variational posterior. Parameters ---------- draws : int Number of random samples. random_seed : int, RandomState or Generator, optional Seed for the random number generator. return_inferencedata : bool Return trace in Arviz format. Returns ------- trace: :class:`pymc.backends.base.MultiTrace` Samples drawn from variational posterior. """ # TODO: add tests for include_transformed case kwargs["log_likelihood"] = False if random_seed is not None: (random_seed,) = _get_seeds_per_chain(random_seed, 1) samples: dict = self.sample_dict_fn(draws, random_seed=random_seed) points = ({name: records[i] for name, records in samples.items()} for i in range(draws)) trace = NDArray( model=self.model, test_point={name: records[0] for name, records in samples.items()}, ) try: trace.setup(draws=draws, chain=0) for point in points: trace.record(point) finally: trace.close() trace = MultiTrace([trace]) if not return_inferencedata: return trace else: return pm.to_inference_data(trace, model=self.model, **kwargs)
@property def ndim(self): return sum(self.collect("ndim")) @property def ddim(self): return sum(self.collect("ddim")) @node_property def symbolic_random(self): return at.concatenate(self.collect("symbolic_random"), axis=-1) def __str__(self): if len(self.groups) < 5: return "Approximation{" + " & ".join(map(str, self.groups)) + "}" else: forprint = self.groups[:2] + ["..."] + self.groups[-2:] return "Approximation{" + " & ".join(map(str, forprint)) + "}" @property def all_histograms(self): return all(isinstance(g, pm.approximations.EmpiricalGroup) for g in self.groups) @property def any_histograms(self): return any(isinstance(g, pm.approximations.EmpiricalGroup) for g in self.groups) @node_property def joint_histogram(self): if not self.all_histograms: raise VariationalInferenceError("%s does not consist of all Empirical approximations") return at.concatenate(self.collect("histogram"), axis=-1) @property def params(self): return sum(self.collect("params"), [])