#   Copyright 2024 - present 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
#
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#   distributed under the License is distributed on an "AS IS" BASIS,
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R"""Operational Variational Inference.

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

from typing import Any, overload

import numpy as np
import pytensor
import pytensor.tensor as pt
import xarray

from pytensor.graph.basic import Variable
from pytensor.graph.replace import graph_replace
from pytensor.scalar.basic import identity as scalar_identity
from pytensor.tensor.elemwise import Elemwise

import pymc as pm

from pymc.backends.base import MultiTrace
from pymc.backends.ndarray import NDArray
from pymc.blocking import DictToArrayBijection
from pymc.initial_point import make_initial_point_fn
from pymc.model import modelcontext
from pymc.pytensorf import (
    SeedSequenceSeed,
    compile,
    constant_fold,
    find_rng_nodes,
    reseed_rngs,
)
from pymc.util import (
    RandomState,
    WithMemoization,
    _get_seeds_per_chain,
    locally_cachedmethod,
    makeiter,
)
from pymc.variational.minibatch_rv import MinibatchRandomVariable, get_scaling
from pymc.variational.updates import adagrad_window
from pymc.vartypes import discrete_types

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


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 _known_scan_ignored_inputs(terms):
    # TODO: remove when scan issue with grads is fixed
    from pymc.data import MinibatchOp
    from pymc.distributions.simulator import SimulatorRV

    return [
        n.owner.inputs[0]
        for n in pytensor.graph.ancestors(terms)
        if n.owner is not None and isinstance(n.owner.op, MinibatchOp | SimulatorRV)
    ]


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):
    """Wrap 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(pt.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,
    ):
        """Construct updates for optimization step after calculating gradients.

        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 = {}
        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 = {}
        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 = {}
        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,
        compile_kwargs=None,
        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
        compile_kwargs: `dict`
            Add kwargs to pytensor.function (e.g. `{'profile': True}`)
        fn_kwargs: dict
            arbitrary kwargs passed to `pytensor.function`

            .. warning:: `fn_kwargs` is deprecated and will be removed in future versions

        more_replacements: `dict`
            Apply custom replacements before calculating gradients

        Returns
        -------
        `pytensor.function`
        """
        if fn_kwargs is not None:
            warnings.warn(
                "`fn_kwargs` is deprecated and will be removed in future versions. Use "
                "`compile_kwargs` instead.",
                DeprecationWarning,
            )
            compile_kwargs = fn_kwargs

        if compile_kwargs is None:
            compile_kwargs = {}
        if score and not self.op.returns_loss:
            raise NotImplementedError(f"{self.op} does not have loss")
        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,
        )
        seed = self.approx.rng.randint(2**30, dtype=np.int64)
        if score:
            step_fn = compile([], updates.loss, updates=updates, random_seed=seed, **compile_kwargs)
        else:
            step_fn = compile([], [], updates=updates, random_seed=seed, **compile_kwargs)
        return step_fn

    @pytensor.config.change_flags(compute_test_value="off")
    def score_function(
        self, sc_n_mc=None, more_replacements=None, compile_kwargs=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
        compile_kwargs: `dict`
            arbitrary kwargs passed to `pytensor.function`
        fn_kwargs: `dict`
            arbitrary kwargs passed to `pytensor.function`

            .. warning:: `fn_kwargs` is deprecated and will be removed in future versions

        Returns
        -------
        pytensor.function
        """
        if fn_kwargs is not None:
            warnings.warn(
                "`fn_kwargs` is deprecated and will be removed in future versions. Use "
                "`compile_kwargs` instead",
                DeprecationWarning,
            )
            compile_kwargs = fn_kwargs

        if compile_kwargs is None:
            compile_kwargs = {}
        if not self.op.returns_loss:
            raise NotImplementedError(f"{self.op} does not have loss")
        if more_replacements is None:
            more_replacements = {}
        loss = self(sc_n_mc, more_replacements=more_replacements)
        seed = self.approx.rng.randint(2**30, dtype=np.int64)
        return compile([], loss, random_seed=seed, **compile_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 = Elemwise(scalar_identity)

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

    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(f"Operator {self} requires TestFunction")
            else:
                if not isinstance(f, TestFunction):
                    f = TestFunction.from_function(f)
        else:
            if f is not None:
                warnings.warn(f"TestFunction for {self} is redundant and removed", stacklevel=3)
            else:
                pass
            f = TestFunction()
        f.setup(self.approx)
        return self.objective_class(self, f)

    def __str__(self):  # pragma: no cover
        """Return a string representation of the object."""
        return f"{self.__class__.__name__}[{self.approx.__class__.__name__}]"


def collect_shared_to_list(params):
    """Get a list from a usable representation of parameters.

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

    Returns
    -------
    List
    """
    if isinstance(params, dict):
        return [
            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(f"Need callable, got {f!r}")
        obj = TestFunction()
        obj.__call__ = f
        return obj


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-block:: 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-block:: 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-block:: 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-block:: 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[str] = frozenset()
    __param_registry: dict[frozenset, Any] = {}
    __name_registry: dict[str, Any] = {}

    @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

    @classmethod
    def group_for_params(cls, params):
        if frozenset(params) not in cls.__param_registry:
            raise KeyError(
                f"No such group for the following params: {params!r}, "
                f"only the following are supported\n\n{cls.__param_registry}"
            )
        return cls.__param_registry[frozenset(params)]

    @classmethod
    def group_for_short_name(cls, name):
        if name.lower() not in cls.__name_registry:
            raise KeyError(
                f"No such group: {name!r}, "
                f"only the following are supported\n\n{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)

    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 = {}
        self.options = options
        self._vfam = vfam
        self.rng = np.random.RandomState(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.randint(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

    @classmethod
    def get_param_spec_for(cls, **kwargs):
        res = {}
        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* - check user params, if correct allocate them and return 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, "
                f"they should be equal, got {givens}, needed {needed}"
            )
        self._user_params = {}
        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] = pt.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 pt.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 pt.vector(name)

    @pytensor.config.change_flags(compute_test_value="off")
    def __init_group__(self, group):
        """Initialize the 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 pt.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 = pt.as_tensor(dim)
        size = pt.as_tensor(size)
        shape = self._new_initial_shape(size, dim, more_replacements)
        # apply optimizations if possible
        if not isinstance(deterministic, Variable):
            if deterministic:
                return pt.ones(shape, dtype) * dist_map
            else:
                return getattr(pt.random, dist_name)(size=shape)
        else:
            sample = getattr(pt.random, dist_name)(size=shape)
            initial = pt.switch(deterministic, pt.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

    @overload
    def set_size_and_deterministic(
        self, node: Variable, s, d: bool, more_replacements: dict | None = None
    ) -> Variable: ...

    @overload
    def set_size_and_deterministic(
        self, node: list[Variable], s, d: bool, more_replacements: dict | None = None
    ) -> list[Variable]: ...

    @pytensor.config.change_flags(compute_test_value="off")
    def set_size_and_deterministic(
        self, node: Variable | list[Variable], s, d: bool, more_replacements: dict | None = None
    ) -> Variable | 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
            PyTensor node(s) 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` or list with applied replacements, ready to use
        """
        flat2rand = self.make_size_and_deterministic_replacements(s, d, more_replacements)
        node_out = graph_replace(node, flat2rand, strict=False)
        assert not (
            set(makeiter(self.input)) & set(pytensor.graph.graph_inputs(makeiter(node_out)))
        )
        try_to_set_test_value(node, node_out, s)
        assert self.symbolic_random not in set(pytensor.graph.graph_inputs(makeiter(node_out)))
        return node_out

    def to_flat_input(self, node):
        """*Dev* - replace vars with flattened view stored in `self.inputs`."""
        return graph_replace(node, self.replacements, strict=False)

    def symbolic_sample_over_posterior(self, node):
        """*Dev* - perform 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 = pt.specify_shape(random, self.symbolic_initial.type.shape)

        def sample(post, *_):
            return graph_replace(node, {self.input: post}, strict=False)

        nodes = pytensor.scan(
            sample,
            random,
            non_sequences=_known_scan_ignored_inputs(makeiter(random)),
            return_updates=False,
        )
        assert self.input not in set(pytensor.graph.graph_inputs(makeiter(nodes)))
        return nodes

    def symbolic_single_sample(self, node):
        """*Dev* - perform 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 graph_replace(node, {self.input: random[0]}, strict=False)

    def make_size_and_deterministic_replacements(self, s, d, more_replacements=None):
        """*Dev* - create 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 = pt.specify_shape(initial, self.symbolic_initial.type.shape)
        if more_replacements:
            initial = graph_replace(initial, more_replacements, strict=False)
        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(
            pt.max(
                [
                    get_scaling(
                        v.owner.inputs[1:],
                        constant_fold([v.owner.inputs[0].shape], raise_not_constant=False),
                    )
                    for v in self.group
                    if isinstance(v.owner.op, MinibatchRandomVariable)
                ]
                + [1.0]  # To avoid empty max
            )
        )
        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):
        """Return a string representation for the object."""
        if self.group is None:
            shp = "undefined"
        else:
            shp = str(self.ddim)
        return f"{self.__class__.__name__}[{shp}]"

    @node_property
    def std(self) -> pt.TensorVariable:
        """Return the standard deviation of the latent variables as an unstructured 1-dimensional tensor variable."""
        raise NotImplementedError()

    @node_property
    def cov(self) -> pt.TensorVariable:
        """Return the covariance between the latent variables as an unstructured 2-dimensional tensor variable."""
        raise NotImplementedError()

    @node_property
    def mean(self) -> pt.TensorVariable:
        """Return the mean of the latent variables as an unstructured 1-dimensional tensor variable."""
        raise NotImplementedError()

    def var_to_data(self, shared: pt.TensorVariable) -> xarray.Dataset:
        """Take a flat 1-dimensional tensor variable and maps it to an xarray data set based on the information in `self.ordering`."""
        # This is somewhat similar to `DictToArrayBijection.rmap`, which doesn't work here since we don't have
        # `RaveledVars` and need to take the information from `self.ordering` instead
        shared_nda = shared.eval()
        result = {}
        for name, s, shape, dtype in self.ordering.values():
            dims = self.model.named_vars_to_dims.get(name, None)
            if dims is not None:
                coords = {d: np.array(self.model.coords[d]) for d in dims}
            else:
                coords = None
            values = shared_nda[s].reshape(shape).astype(dtype)
            result[name] = xarray.DataArray(values, coords=coords, dims=dims, name=name)
        return xarray.Dataset(result)

    @property
    def mean_data(self) -> xarray.Dataset:
        """Mean of the latent variables as an xarray Dataset."""
        return self.var_to_data(self.mean)

    @property
    def std_data(self) -> xarray.Dataset:
        """Standard deviation of the latent variables as an xarray Dataset."""
        return self.var_to_data(self.std)


group_for_params = Group.group_for_params
group_for_short_name = Group.group_for_short_name


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`
    """

    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 = []
        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"))

    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 = pt.max(
            self.collect("symbolic_normalizing_constant")
            + [
                get_scaling(
                    obs.owner.inputs[1:],
                    constant_fold([obs.owner.inputs[0].shape], raise_not_constant=False),
                )
                for obs in self.model.observed_RVs
                if isinstance(obs.owner.op, MinibatchRandomVariable)
            ]
        )
        t = pt.switch(self._scale_cost_to_minibatch, t, pt.constant(1, dtype=t.dtype))
        return pm.floatX(t)

    @node_property
    def symbolic_logq(self):
        """*Dev* - collects `symbolic_logq` for all groups."""
        return pt.add(*self.collect("symbolic_logq"))

    @node_property
    def logq(self):
        """*Dev* - collects `logQ` for all groups."""
        return pt.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)
        )

    def make_size_and_deterministic_replacements(self, s, d, more_replacements=None):
        """*Dev* - create 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

    @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 = graph_replace(node, optimizations, strict=False)
        node = graph_replace(node, flat2rand, strict=False)
        assert not (set(self.symbolic_randoms) & set(pytensor.graph.graph_inputs(makeiter(node))))
        try_to_set_test_value(_node, node, s)
        return node

    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 = graph_replace(node, more_replacements, strict=False)
        return graph_replace(node, self.replacements, strict=False)

    def symbolic_sample_over_posterior(self, node, more_replacements=None):
        """*Dev* - perform 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)

        def sample(*post):
            return graph_replace(node, dict(zip(self.inputs, post)), strict=False)

        nodes = pytensor.scan(
            sample,
            self.symbolic_randoms,
            non_sequences=_known_scan_ignored_inputs(makeiter(node)),
            return_updates=False,
        )
        assert not (set(self.inputs) & set(pytensor.graph.graph_inputs(makeiter(nodes))))
        return nodes

    def symbolic_single_sample(self, node, more_replacements=None):
        """*Dev* - perform 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 graph_replace(node, dict(zip(inp, post)), strict=False)

    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

    @pytensor.config.change_flags(compute_test_value="off")
    def sample_node(self, node, size=None, deterministic=False, more_replacements=None):
        """Sample 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 = graph_replace(node, more_replacements, strict=False)
        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

    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(f"{name!r} not found")
        return found

    @node_property
    def sample_dict_fn(self):
        s = pt.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([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 dict(zip(names, _samples))

        return inner

    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: np.asarray(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()

        multi_trace = MultiTrace([trace])
        if not return_inferencedata:
            return multi_trace
        else:
            return pm.to_inference_data(multi_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 pt.concatenate(self.collect("symbolic_random"), axis=-1)

    def __str__(self):
        """Return a string representation of the object."""
        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 pt.concatenate(self.collect("histogram"), axis=-1)

    @property
    def params(self):
        return list(itertools.chain.from_iterable(self.collect("params")))
