Source code for pymc.variational.opvi

#   Copyright 2020 The PyMC Developers
#
#   you may not use this file except in compliance with the License.
#   You may obtain a copy of the License at
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#   Unless required by applicable law or agreed to in writing, software
#   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
#   See the License for the specific language governing permissions and

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.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):

class AEVBInferenceError(VariationalInferenceError, TypeError):

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

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)

self,
obj_n_mc=None,
tf_n_mc=None,
more_obj_params=None,
more_tf_params=None,
more_replacements=None,
):
"""Calculate gradients for objective function, test function and then

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_replacements : dict
Apply custom replacements before calculating gradients

Returns
-------
:class:ObjectiveUpdates
"""
if self.test_params:
tf_n_mc=tf_n_mc,
test_optimizer=test_optimizer,
more_tf_params=more_tf_params,
more_replacements=more_replacements,
)
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)
obj_n_mc=obj_n_mc,
obj_optimizer=obj_optimizer,
more_obj_params=more_obj_params,
more_replacements=more_replacements,
)

self,
tf_n_mc=None,
more_tf_params=None,
more_replacements=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
)

self,
obj_n_mc=None,
more_obj_params=None,
more_replacements=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
)
if self.op.returns_loss:

@pytensor.config.change_flags(compute_test_value="off")
def step_function(
self,
obj_n_mc=None,
tf_n_mc=None,
more_obj_params=None,
more_tf_params=None,
more_replacements=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
Optimizer that is used for objective params
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
total_grad_norm_constraint: float
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)
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_replacements=more_replacements,
)
if score:
else:
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)

--------
: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

--------
: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"""

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

@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:
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"), [])