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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 inverence 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 forth 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)
"""
import collections
import itertools
import warnings
import numpy as np
import theano
import theano.tensor as tt
import pymc3 as pm
from pymc3.util import get_transformed
from .updates import adagrad_window
from ..blocking import (
ArrayOrdering, DictToArrayBijection, VarMap
)
from ..model import modelcontext
from ..theanof import tt_rng, change_flags, identity
from ..util import get_default_varnames
from ..memoize import WithMemoization, memoize
__all__ = [
'ObjectiveFunction',
'Operator',
'TestFunction',
'Group',
'Approximation'
]
class VariationalInferenceError(Exception):
"""Exception for VI specific cases"""
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"""
class BatchedGroupError(GroupError):
"""Error with batched variables"""
class LocalGroupError(BatchedGroupError, AEVBInferenceError):
"""Error raised in case of bad local_rv usage"""
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):
return property(memoize(change_flags(compute_test_value='off')(append_name(f)(fn)), bound=True))
return wrapper
else:
return property(memoize(change_flags(compute_test_value='off')(f), bound=True))
@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 = theano.compile.view_op(tt.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(theano.OrderedUpdates):
"""OrderedUpdates extension for storing loss
"""
loss = None
def _warn_not_used(smth, where):
warnings.warn('`%s` is not used for %s and ignored' % (smth, where))
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, tf):
self.op = op
self.tf = tf
obj_params = property(lambda self: self.op.approx.params)
test_params = property(lambda self: self.tf.params)
approx = property(lambda self: self.op.approx)
def updates(self, obj_n_mc=None, tf_n_mc=None, obj_optimizer=adagrad_window, test_optimizer=adagrad_window,
more_obj_params=None, more_tf_params=None, more_updates=None,
more_replacements=None, total_grad_norm_constraint=None):
"""Calculate gradients for objective function, test function and then
constructs updates for optimization step
Parameters
----------
obj_n_mc : `int`
Number of monte carlo samples used for approximation of objective gradients
tf_n_mc : `int`
Number of monte carlo samples used for approximation of test function gradients
obj_optimizer : function (loss, params) -> updates
Optimizer that is used for objective params
test_optimizer : function (loss, params) -> updates
Optimizer that is used for test function params
more_obj_params : `list`
Add custom params for objective optimizer
more_tf_params : `list`
Add custom params for test function optimizer
more_updates : `dict`
Add custom updates to resulting updates
more_replacements : `dict`
Apply custom replacements before calculating gradients
total_grad_norm_constraint : `float`
Bounds gradient norm, prevents exploding gradient problem
Returns
-------
:class:`ObjectiveUpdates`
"""
if more_updates is None:
more_updates = dict()
resulting_updates = ObjectiveUpdates()
if self.test_params:
self.add_test_updates(
resulting_updates,
tf_n_mc=tf_n_mc,
test_optimizer=test_optimizer,
more_tf_params=more_tf_params,
more_replacements=more_replacements,
total_grad_norm_constraint=total_grad_norm_constraint
)
else:
if tf_n_mc is not None:
_warn_not_used('tf_n_mc', self.op)
if more_tf_params:
_warn_not_used('more_tf_params', self.op)
self.add_obj_updates(
resulting_updates,
obj_n_mc=obj_n_mc,
obj_optimizer=obj_optimizer,
more_obj_params=more_obj_params,
more_replacements=more_replacements,
total_grad_norm_constraint=total_grad_norm_constraint
)
resulting_updates.update(more_updates)
return resulting_updates
def add_test_updates(self, updates, tf_n_mc=None, test_optimizer=adagrad_window,
more_tf_params=None, more_replacements=None,
total_grad_norm_constraint=None):
if more_tf_params is None:
more_tf_params = []
if more_replacements is None:
more_replacements = dict()
tf_target = self(tf_n_mc, more_tf_params=more_tf_params, more_replacements=more_replacements)
grads = pm.updates.get_or_compute_grads(tf_target, self.obj_params + more_tf_params)
if total_grad_norm_constraint is not None:
grads = pm.total_norm_constraint(grads, total_grad_norm_constraint)
updates.update(
test_optimizer(
grads,
self.test_params +
more_tf_params))
def add_obj_updates(self, updates, obj_n_mc=None, obj_optimizer=adagrad_window,
more_obj_params=None, more_replacements=None,
total_grad_norm_constraint=None):
if more_obj_params is None:
more_obj_params = []
if more_replacements is None:
more_replacements = dict()
obj_target = self(obj_n_mc, more_obj_params=more_obj_params, more_replacements=more_replacements)
grads = pm.updates.get_or_compute_grads(obj_target, self.obj_params + more_obj_params)
if total_grad_norm_constraint is not None:
grads = pm.total_norm_constraint(grads, total_grad_norm_constraint)
updates.update(
obj_optimizer(
grads,
self.obj_params +
more_obj_params))
if self.op.returns_loss:
updates.loss = obj_target
@change_flags(compute_test_value='off')
def step_function(self, obj_n_mc=None, tf_n_mc=None,
obj_optimizer=adagrad_window, test_optimizer=adagrad_window,
more_obj_params=None, more_tf_params=None,
more_updates=None, more_replacements=None,
total_grad_norm_constraint=None,
score=False, fn_kwargs=None):
R"""Step function that should be called on each optimization step.
Generally it solves the following problem:
.. math::
\mathbf{\lambda^{\*}} = \inf_{\lambda} \sup_{\theta} t(\mathbb{E}_{\lambda}[(O^{p,q}f_{\theta})(z)])
Parameters
----------
obj_n_mc : `int`
Number of monte carlo samples used for approximation of objective gradients
tf_n_mc : `int`
Number of monte carlo samples used for approximation of test function gradients
obj_optimizer : function (grads, params) -> updates
Optimizer that is used for objective params
test_optimizer : function (grads, params) -> updates
Optimizer that is used for test function params
more_obj_params : `list`
Add custom params for objective optimizer
more_tf_params : `list`
Add custom params for test function optimizer
more_updates : `dict`
Add custom updates to resulting updates
total_grad_norm_constraint : `float`
Bounds gradient norm, prevents exploding gradient problem
score : `bool`
calculate loss on each step? Defaults to False for speed
fn_kwargs : `dict`
Add kwargs to theano.function (e.g. `{'profile': True}`)
more_replacements : `dict`
Apply custom replacements before calculating gradients
Returns
-------
`theano.function`
"""
if fn_kwargs is None:
fn_kwargs = {}
if score and not self.op.returns_loss:
raise NotImplementedError('%s does not have loss' % self.op)
updates = self.updates(obj_n_mc=obj_n_mc, tf_n_mc=tf_n_mc,
obj_optimizer=obj_optimizer,
test_optimizer=test_optimizer,
more_obj_params=more_obj_params,
more_tf_params=more_tf_params,
more_updates=more_updates,
more_replacements=more_replacements,
total_grad_norm_constraint=total_grad_norm_constraint)
if score:
step_fn = theano.function(
[], updates.loss, updates=updates, **fn_kwargs)
else:
step_fn = theano.function([], None, updates=updates, **fn_kwargs)
return step_fn
@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 `theano.function`
Returns
-------
theano.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 theano.function([], loss, **fn_kwargs)
@change_flags(compute_test_value='off')
def __call__(self, nmc, **kwargs):
if 'more_tf_params' in kwargs:
m = -1.
else:
m = 1.
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 not self.supports_aevb and approx.has_local:
raise AEVBInferenceError('%s does not support AEVB, '
'please change inference method' % self)
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], theano.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
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 PyMC3 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 :
PyMC3 Model
local : bool
Indicates whether this group is local. Cannot be passed without `params`.
Such group should have only one variable
rowwise : bool
Indicates whether this group is independently parametrized over first dim.
Such group should have only one variable
options : dict
Special options for the group
kwargs : Other kwargs for the group
Notes
-----
Group instance/class has some important constants:
- **supports_batched**
Determines whether such variational family can be used for AEVB or rowwise approx.
AEVB approx is such approx that somehow depends on input data. It can be treated
as conditional distribution. You can see more about in the corresponding paper
mentioned in references.
Rowwise mode is a special case approximation that treats every 'row', of a tensor as
independent from each other. Some distributions can't do that by
definition e.g. :class:`Empirical` that consists of particles only.
- **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`
- `{0, 1, 2, 3, ..., k-1}`: :class:`NormalizingFlowGroup` of depth `k`
NormalizingFlows have other parameters than ordinary groups and should be
passed as nested dicts with the following keys:
- `{'u', 'w', 'b'}`: :class:`PlanarFlow`
- `{'a', 'b', 'z_ref'}`: :class:`RadialFlow`
- `{'loc'}`: :class:`LocFlow`
- `{'rho'}`: :class:`ScaleFlow`
- `{'v'}`: :class:`HouseholderFlow`
Note that all integer keys should be present in the dictionary. An example
of NormalizingFlow initialization can be found below.
**Using AEVB**
Autoencoding variational Bayes is a powerful tool to get conditional :math:`q(\lambda|X)` distribution
on latent variables. It is well supported by PyMC3 and all you need is to provide a dictionary
with well shaped variational parameters, the correct approximation will be autoselected as mentioned
in section above. However we have some implementation restrictions in AEVB. They require autoencoded
variable to have first dimension as *batch* dimension and other dimensions should stay fixed.
With this assumptions it is possible to generalize all variational approximation families as
batched approximations that have flexible parameters and leading axis.
Only single variable local group is supported. Params are required.
>>> # for mean field
>>> group = Group([latent3], params=dict(mu=my_mu, rho=my_rho), local=True)
>>> # or for full rank
>>> group = Group([latent3], params=dict(mu=my_mu, L_tril=my_L_tril), local=True)
- An Approximation class is selected automatically based on the keys in dict.
- `my_mu` and `my_rho` are usually estimated with neural network or function approximator.
**Using Row-Wise Group**
Batch groups have independent row wise approximations, thus using batched
mean field will give no effect. It is more interesting if you want each row of a matrix
to be parametrized independently with normalizing flow or full rank gaussian.
To tell :class:`Group` that group is batched you need set `batched` kwarg as `True`.
Only single variable group is allowed due to implementation details.
>>> group = Group([latent3], vfam='fr', rowwise=True) # 'fr' is alias for 'full_rank'
The resulting approximation for this variable will have the following structure
.. math::
latent3_{i, \dots} \sim \mathcal{N}(\mu_i, \Sigma_i) \forall i
**Note**: Using rowwise and user-parametrized approximation is ok, but
shape should be checked beforehand, it is impossible to infer it by PyMC3
**Normalizing Flow Group**
In case you use simple initialization pattern using `vfam` you'll not meet any changes.
Passing flow formula to `vfam` you'll get correct flow parametrization for group
.. code:: python
>>> group = Group([latent3], vfam='scale-hh*5-radial*4-loc')
**Note**: Consider passing location flow as the last one and scale as the first one for stable inference.
Rowwise normalizing flow is supported as well
.. code:: python
>>> group = Group([latent3], vfam='scale-hh*2-radial-loc', rowwise=True)
Custom parameters for normalizing flow can be a real trouble for the first time.
They have quite different format from the rest variational families.
.. code:: python
>>> # int is used as key, it also tells the flow position
... flow_params = {
... # `rho` parametrizes scale flow, softplus is used to map (-inf; inf) -> (0, inf)
... 0: dict(rho=my_scale),
... 1: dict(v=my_v1), # Householder Flow, `v` is parameter name from the original paper
... 2: dict(v=my_v2), # do not miss any number in dict, or else error is raised
... 3: dict(a=my_a, b=my_b, z_ref=my_z_ref), # Radial flow
... 4: dict(loc=my_loc) # Location Flow
... }
... group = Group([latent3], params=flow_params)
... # local=True can be added in case you do AEVB inference
... group = Group([latent3], params=flow_params, local=True)
**Delayed Initialization**
When you have a lot of latent variables it is impractical to do it all manually.
To make life much simpler, You can pass `None` instead of list of variables. That case
you'll not create shared parameters until you pass all collected groups to
Approximation object that collects all the groups together and checks that every group is
correctly initialized. For those groups which have group equal to `None` it will collect all
the rest variables not covered by other groups and perform delayed init.
.. code:: python
>>> group_1 = Group([latent1], vfam='fr') # latent1 has full rank approximation
>>> group_other = Group(None, vfam='mf') # other variables have mean field Q
>>> approx = Approximation([group_1, group_other])
**Summing Up**
When you have created all the groups they need to pass all the groups to :class:`Approximation`.
It does not accept any other parameter rather than `groups`
.. code:: python
>>> approx = Approximation(my_groups)
See Also
--------
:class:`Approximation`
References
----------
- Kingma, D. P., & Welling, M. (2014).
`Auto-Encoding Variational Bayes. stat, 1050, 1. <https://arxiv.org/abs/1312.6114>`_
"""
# needs to be defined in init
shared_params = None
symbolic_initial = None
replacements = None
input = None
# defined by approximation
supports_batched = True
has_logq = True
# some important defaults
initial_dist_name = 'normal'
initial_dist_map = 0.
# for handy access using class methods
__param_spec__ = dict()
short_name = ''
alias_names = frozenset()
__param_registry = dict()
__name_registry = dict()
@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 pm.variational.flows.seems_like_flow_params(params):
return pm.variational.approximations.NormalizingFlowGroup
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)]
@classmethod
def group_for_short_name(cls, name):
if pm.variational.flows.seems_like_formula(name):
return pm.variational.approximations.NormalizingFlowGroup
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)
def __init__(self, group,
vfam=None,
params=None,
random_seed=None,
model=None,
local=False,
rowwise=False,
options=None,
**kwargs):
if local and not self.supports_batched:
raise LocalGroupError('%s does not support local groups' % self.__class__)
if local and rowwise:
raise LocalGroupError('%s does not support local grouping in rowwise mode')
if isinstance(vfam, str):
vfam = vfam.lower()
if options is None:
options = dict()
self.options = options
self._vfam = vfam
self._local = local
self._batched = rowwise
self._rng = tt_rng(random_seed)
model = modelcontext(model)
self.model = model
self.group = group
self.user_params = params
self._user_params = None
# 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)
@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]
if self.local:
shape = (-1, ) + shape
elif self.batched:
shape = (self.bdim, ) + shape
self._user_params[name] = tt.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
"""
if self.batched:
return tt.tensor3(name)
else:
return tt.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
"""
if self.batched:
return tt.matrix(name)
else:
return tt.vector(name)
@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
if self.batched and len(group) > 1:
if self.local: # better error message
raise LocalGroupError('Local groups with more than 1 variable are not supported')
else:
raise BatchedGroupError('Batched groups with more than 1 variable are not supported')
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
self.ordering = ArrayOrdering([])
self.replacements = dict()
self.group = [get_transformed(var) for var in self.group]
for var in self.group:
if isinstance(var.distribution, pm.Discrete):
raise ParametrizationError('Discrete variables are not supported by VI: {}'
.format(var))
begin = self.ddim
if self.batched:
if var.ndim < 1:
if self.local:
raise LocalGroupError('Local variable should not be scalar')
else:
raise BatchedGroupError('Batched variable should not be scalar')
self.ordering.size += (np.prod(var.dshape[1:])).astype(int)
if self.local:
shape = (-1, ) + var.dshape[1:]
else:
shape = var.dshape
else:
self.ordering.size += var.dsize
shape = var.dshape
end = self.ordering.size
vmap = VarMap(var.name, slice(begin, end), shape, var.dtype)
self.ordering.vmap.append(vmap)
self.ordering.by_name[vmap.var] = vmap
vr = self.input[..., vmap.slc].reshape(shape).astype(vmap.dtyp)
vr.name = vmap.var + '_vi_replacement'
self.replacements[var] = vr
self.bij = DictToArrayBijection(self.ordering, {})
def _finalize_init(self):
"""*Dev* - clean up after init
"""
del self._kwargs
local = property(lambda self: self._local)
batched = property(lambda self: self._local or self._batched)
@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
"""
if self.batched:
bdim = tt.as_tensor(self.bdim)
bdim = theano.clone(bdim, more_replacements)
return tt.stack([size, bdim, dim])
else:
return tt.stack([size, dim])
@node_property
def bdim(self):
if not self.local:
if self.batched:
return self.ordering.vmap[0].shp[0]
else:
return 1
else:
return next(iter(self.params_dict.values())).shape[0]
@node_property
def ndim(self):
return self.ordering.size * self.bdim
@property
def ddim(self):
return self.ordering.size
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, tt.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 = tt.as_tensor(dim)
size = tt.as_tensor(size)
shape = self._new_initial_shape(size, dim, more_replacements)
# apply optimizations if possible
if not isinstance(deterministic, tt.Variable):
if deterministic:
return tt.ones(shape, dtype) * dist_map
else:
return getattr(self._rng, dist_name)(shape)
else:
sample = getattr(self._rng, dist_name)(shape)
initial = tt.switch(
deterministic,
tt.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
@node_property
def symbolic_random2d(self):
"""*Dev* - `self.symbolic_random` flattened to matrix"""
if self.batched:
return self.symbolic_random.flatten(2)
else:
return self.symbolic_random
@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`
Theano 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 = theano.clone(node, flat2rand)
try_to_set_test_value(node, node_out, s)
return node_out
def to_flat_input(self, node):
"""*Dev* - replace vars with flattened view stored in `self.inputs`
"""
return theano.clone(node, self.replacements)
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 = tt.patternbroadcast(random, self.symbolic_initial.broadcastable)
def sample(post):
return theano.clone(node, {self.input: post})
nodes, _ = theano.scan(
sample, random)
return nodes
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)
random = tt.patternbroadcast(random, self.symbolic_initial.broadcastable)
return theano.clone(
node, {self.input: random[0]}
)
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 = tt.patternbroadcast(initial, self.symbolic_initial.broadcastable)
if more_replacements:
initial = theano.clone(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(
tt.max([v.scaling 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`
"""
if self.local:
s = self.group[0].scaling
s = self.to_flat_input(s)
s = self.symbolic_single_sample(s)
return self.symbolic_logq_not_scaled * s
else:
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)
if self.local:
shp = 'None, ' + shp
elif self.batched:
shp = str(self.bdim) + ', ' + shp
return '{cls}[{shp}]'.format(shp=shp, cls=self.__class__.__name__)
@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
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:`NormalizingFlow`
- :class:`Empirical`
Single group accepts `local_rv` keyword with dict mapping PyMC3 variables
to their local Group parameters dict
See Also
--------
:class:`Group`
"""
def __init__(self, groups, model=None):
self._scale_cost_to_minibatch = theano.shared(np.int8(1))
model = modelcontext(model)
if not model.free_RVs:
raise TypeError('Model does not have FreeRVs')
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)
if set(model.free_RVs) - seen:
if rest is None:
raise GroupError('No approximation is specified for the rest variables')
else:
rest.__init_group__(list(set(model.free_RVs) - seen))
self.groups.append(rest)
self.model = model
@property
def has_logq(self):
return all(self.collect('has_logq'))
def collect(self, item, part='total'):
if part == 'total':
return [getattr(g, item) for g in self.groups]
elif part == 'local':
return [getattr(g, item) for g in self.groups if g.local]
elif part == 'global':
return [getattr(g, item) for g in self.groups if not g.local]
elif part == 'batched':
return [getattr(g, item) for g in self.groups if g.batched]
else:
raise ValueError("unknown part %s, expected {'local', 'global', 'total', 'batched'}")
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 = tt.max(
self.collect('symbolic_normalizing_constant') + [
var.scaling for var in self.model.observed_RVs
])
t = tt.switch(self._scale_cost_to_minibatch, t,
tt.constant(1, dtype=t.dtype))
return pm.floatX(t)
@node_property
def symbolic_logq(self):
"""*Dev* - collects `symbolic_logq` for all groups"""
return tt.add(*self.collect('symbolic_logq'))
@node_property
def logq(self):
"""*Dev* - collects `logQ` for all groups"""
return tt.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 `theano.scan`"""
varlogp_s, datalogp_s = self.symbolic_sample_over_posterior(
[self.model.varlogpt, self.model.datalogpt])
return varlogp_s, datalogp_s # both shape (s,)
@node_property
def sized_symbolic_varlogp(self):
"""*Dev* - computes sampled prior term from model via `theano.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 `theano.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 `theano.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 `theano.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 `theano.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 `theano.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 `theano.scan`"""
varlogp, datalogp = self.symbolic_single_sample(
[self.model.varlogpt, self.model.datalogpt])
return varlogp, datalogp
@node_property
def single_symbolic_varlogp(self):
"""*Dev* - for single MC sample estimate of :math:`E_{q}(prior term)` `theano.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)` `theano.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)` `theano.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* - 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
@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`
Theano 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 = theano.clone(node, optimizations)
node = theano.clone(node, flat2rand)
try_to_set_test_value(_node, node, s)
return node
def to_flat_input(self, node):
"""*Dev* - replace vars with flattened view stored in `self.inputs`
"""
return theano.clone(node, self.replacements)
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)
def sample(*post):
return theano.clone(node, dict(zip(self.inputs, post)))
nodes, _ = theano.scan(
sample, self.symbolic_randoms)
return nodes
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)
post = [v[0] for v in self.symbolic_randoms]
inp = self.inputs
return theano.clone(
node, dict(zip(inp, post))
)
def get_optimization_replacements(self, s, d):
"""*Dev* - optimizations for logP. If sample size is static and equal to 1:
then `theano.scan` MC estimate is replaced with single sample without call to `theano.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
@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 : Theano Variables (or Theano 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
node = theano.clone(node, more_replacements)
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, more_replacements)
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 `theano.scan`.
This node still needs :func:`set_size_and_deterministic` to be evaluated
"""
def vars_names(vs):
return {v.name for v in vs}
for vars_, random, ordering in zip(
self.collect('group'),
self.symbolic_randoms,
self.collect('ordering')):
if name in vars_names(vars_):
name_, slc, shape, dtype = ordering[name]
found = random[..., slc].reshape((random.shape[0], ) + shape).astype(dtype)
found.name = name + '_vi_random_slice'
break
else:
raise KeyError('%r not found' % name)
return found
@property
@memoize(bound=True)
@change_flags(compute_test_value='off')
def sample_dict_fn(self):
s = tt.iscalar()
names = [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 = theano.function([s], sampled)
def inner(draws=100):
_samples = sample_fn(draws)
return dict([(v_.name, s_) for v_, s_ in zip(self.model.free_RVs, _samples)])
return inner
def sample(self, draws=500, include_transformed=True):
"""Draw samples from variational posterior.
Parameters
----------
draws : `int`
Number of random samples.
include_transformed : `bool`
If True, transformed variables are also sampled. Default is False.
Returns
-------
trace : :class:`pymc3.backends.base.MultiTrace`
Samples drawn from variational posterior.
"""
vars_sampled = get_default_varnames(self.model.unobserved_RVs,
include_transformed=include_transformed)
samples = self.sample_dict_fn(draws) # type: dict
points = ({name: records[i] for name, records in samples.items()} for i in range(draws))
trace = pm.sampling.NDArray(model=self.model, vars=vars_sampled, 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()
return pm.sampling.MultiTrace([trace])
@property
def ndim(self):
return sum(self.collect('ndim'))
@property
def ddim(self):
return sum(self.collect('ddim'))
@property
def has_local(self):
return any(self.collect('local'))
@property
def has_global(self):
return any(not c for c in self.collect('local'))
@property
def has_batched(self):
return any(not c for c in self.collect('batched'))
@node_property
def symbolic_random(self):
return tt.concatenate(self.collect('symbolic_random2d'), 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 tt.concatenate(self.collect('histogram'), axis=-1)
@property
def params(self):
return sum(self.collect('params'), [])