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import collections
import functools
import itertools
import threading
import warnings
import numpy as np
from pandas import Series
import scipy.sparse as sps
import theano.sparse as sparse
from theano import theano, tensor as tt
from theano.tensor.var import TensorVariable
from pymc3.theanof import set_theano_conf, floatX
import pymc3 as pm
from pymc3.math import flatten_list
from .memoize import memoize, WithMemoization
from .theanof import gradient, hessian, inputvars, generator
from .vartypes import typefilter, discrete_types, continuous_types, isgenerator
from .blocking import DictToArrayBijection, ArrayOrdering
from .util import get_transformed_name
__all__ = [
'Model', 'Factor', 'compilef', 'fn', 'fastfn', 'modelcontext',
'Point', 'Deterministic', 'Potential'
]
FlatView = collections.namedtuple('FlatView', 'input, replacements, view')
class InstanceMethod:
"""Class for hiding references to instance methods so they can be pickled.
>>> self.method = InstanceMethod(some_object, 'method_name')
"""
def __init__(self, obj, method_name):
self.obj = obj
self.method_name = method_name
def __call__(self, *args, **kwargs):
return getattr(self.obj, self.method_name)(*args, **kwargs)
def incorporate_methods(source, destination, methods, default=None,
wrapper=None, override=False):
"""
Add attributes to a destination object which points to
methods from from a source object.
Parameters
----------
source : object
The source object containing the methods.
destination : object
The destination object for the methods.
methods : list of str
Names of methods to incorporate.
default : object
The value used if the source does not have one of the listed methods.
wrapper : function
An optional function to allow the source method to be
wrapped. Should take the form my_wrapper(source, method_name)
and return a single value.
override : bool
If the destination object already has a method/attribute
an AttributeError will be raised if override is False (the default).
"""
for method in methods:
if hasattr(destination, method) and not override:
raise AttributeError("Cannot add method {!r}".format(method) +
"to destination object as it already exists. "
"To prevent this error set 'override=True'.")
if hasattr(source, method):
if wrapper is None:
setattr(destination, method, getattr(source, method))
else:
setattr(destination, method, wrapper(source, method))
else:
setattr(destination, method, None)
def get_named_nodes_and_relations(graph):
"""Get the named nodes in a theano graph (i.e., nodes whose name
attribute is not None) along with their relationships (i.e., the
node's named parents, and named children, while skipping unnamed
intermediate nodes)
Parameters
----------
graph - a theano node
Returns:
leaf_nodes: A dictionary of name:node pairs, of the named nodes that
are also leafs of the graph
node_parents: A dictionary of node:set([parents]) pairs. Each key is
a theano named node, and the corresponding value is the set of
theano named nodes that are parents of the node. These parental
relations skip unnamed intermediate nodes.
node_children: A dictionary of node:set([children]) pairs. Each key
is a theano named node, and the corresponding value is the set
of theano named nodes that are children of the node. These child
relations skip unnamed intermediate nodes.
"""
if graph.name is not None:
node_parents = {graph: set()}
node_children = {graph: set()}
else:
node_parents = {}
node_children = {}
return _get_named_nodes_and_relations(graph, None, {}, node_parents, node_children)
def _get_named_nodes_and_relations(graph, parent, leaf_nodes,
node_parents, node_children):
if getattr(graph, 'owner', None) is None: # Leaf node
if graph.name is not None: # Named leaf node
leaf_nodes.update({graph.name: graph})
if parent is not None: # Is None for the root node
try:
node_parents[graph].add(parent)
except KeyError:
node_parents[graph] = {parent}
node_children[parent].add(graph)
else:
node_parents[graph] = set()
# Flag that the leaf node has no children
node_children[graph] = set()
else: # Intermediate node
if graph.name is not None: # Intermediate named node
if parent is not None: # Is only None for the root node
try:
node_parents[graph].add(parent)
except KeyError:
node_parents[graph] = {parent}
node_children[parent].add(graph)
else:
node_parents[graph] = set()
# The current node will be set as the parent of the next
# nodes only if it is a named node
parent = graph
# Init the nodes children to an empty set
node_children[graph] = set()
for i in graph.owner.inputs:
temp_nodes, temp_inter, temp_tree = \
_get_named_nodes_and_relations(i, parent, leaf_nodes,
node_parents, node_children)
leaf_nodes.update(temp_nodes)
node_parents.update(temp_inter)
node_children.update(temp_tree)
return leaf_nodes, node_parents, node_children
class Context:
"""Functionality for objects that put themselves in a context using
the `with` statement.
"""
contexts = threading.local()
def __enter__(self):
type(self).get_contexts().append(self)
# self._theano_config is set in Model.__new__
if hasattr(self, '_theano_config'):
self._old_theano_config = set_theano_conf(self._theano_config)
return self
def __exit__(self, typ, value, traceback):
type(self).get_contexts().pop()
# self._theano_config is set in Model.__new__
if hasattr(self, '_old_theano_config'):
set_theano_conf(self._old_theano_config)
@classmethod
def get_contexts(cls):
# no race-condition here, cls.contexts is a thread-local object
# be sure not to override contexts in a subclass however!
if not hasattr(cls.contexts, 'stack'):
cls.contexts.stack = []
return cls.contexts.stack
@classmethod
def get_context(cls):
"""Return the deepest context on the stack."""
try:
return cls.get_contexts()[-1]
except IndexError:
raise TypeError("No context on context stack")
def modelcontext(model):
"""return the given model or try to find it in the context if there was
none supplied.
"""
if model is None:
return Model.get_context()
return model
class Factor:
"""Common functionality for objects with a log probability density
associated with them.
"""
def __init__(self, *args, **kwargs):
super().__init__(*args, **kwargs)
@property
def logp(self):
"""Compiled log probability density function"""
return self.model.fn(self.logpt)
@property
def logp_elemwise(self):
return self.model.fn(self.logp_elemwiset)
def dlogp(self, vars=None):
"""Compiled log probability density gradient function"""
return self.model.fn(gradient(self.logpt, vars))
def d2logp(self, vars=None):
"""Compiled log probability density hessian function"""
return self.model.fn(hessian(self.logpt, vars))
@property
def logp_nojac(self):
return self.model.fn(self.logp_nojact)
def dlogp_nojac(self, vars=None):
"""Compiled log density gradient function, without jacobian terms."""
return self.model.fn(gradient(self.logp_nojact, vars))
def d2logp_nojac(self, vars=None):
"""Compiled log density hessian function, without jacobian terms."""
return self.model.fn(hessian(self.logp_nojact, vars))
@property
def fastlogp(self):
"""Compiled log probability density function"""
return self.model.fastfn(self.logpt)
def fastdlogp(self, vars=None):
"""Compiled log probability density gradient function"""
return self.model.fastfn(gradient(self.logpt, vars))
def fastd2logp(self, vars=None):
"""Compiled log probability density hessian function"""
return self.model.fastfn(hessian(self.logpt, vars))
@property
def fastlogp_nojac(self):
return self.model.fastfn(self.logp_nojact)
def fastdlogp_nojac(self, vars=None):
"""Compiled log density gradient function, without jacobian terms."""
return self.model.fastfn(gradient(self.logp_nojact, vars))
def fastd2logp_nojac(self, vars=None):
"""Compiled log density hessian function, without jacobian terms."""
return self.model.fastfn(hessian(self.logp_nojact, vars))
@property
def logpt(self):
"""Theano scalar of log-probability of the model"""
if getattr(self, 'total_size', None) is not None:
logp = self.logp_sum_unscaledt * self.scaling
else:
logp = self.logp_sum_unscaledt
if self.name is not None:
logp.name = '__logp_%s' % self.name
return logp
@property
def logp_nojact(self):
"""Theano scalar of log-probability, excluding jacobian terms."""
if getattr(self, 'total_size', None) is not None:
logp = tt.sum(self.logp_nojac_unscaledt) * self.scaling
else:
logp = tt.sum(self.logp_nojac_unscaledt)
if self.name is not None:
logp.name = '__logp_%s' % self.name
return logp
class InitContextMeta(type):
"""Metaclass that executes `__init__` of instance in it's context"""
def __call__(cls, *args, **kwargs):
instance = cls.__new__(cls, *args, **kwargs)
with instance: # appends context
instance.__init__(*args, **kwargs)
return instance
def withparent(meth):
"""Helper wrapper that passes calls to parent's instance"""
def wrapped(self, *args, **kwargs):
res = meth(self, *args, **kwargs)
if getattr(self, 'parent', None) is not None:
getattr(self.parent, meth.__name__)(*args, **kwargs)
return res
# Unfortunately functools wrapper fails
# when decorating built-in methods so we
# need to fix that improper behaviour
wrapped.__name__ = meth.__name__
return wrapped
class treelist(list):
"""A list that passes mutable extending operations used in Model
to parent list instance.
Extending treelist you will also extend its parent
"""
def __init__(self, iterable=(), parent=None):
super().__init__(iterable)
assert isinstance(parent, list) or parent is None
self.parent = parent
if self.parent is not None:
self.parent.extend(self)
# typechecking here works bad
append = withparent(list.append)
__iadd__ = withparent(list.__iadd__)
extend = withparent(list.extend)
def tree_contains(self, item):
if isinstance(self.parent, treedict):
return (list.__contains__(self, item) or
self.parent.tree_contains(item))
elif isinstance(self.parent, list):
return (list.__contains__(self, item) or
self.parent.__contains__(item))
else:
return list.__contains__(self, item)
def __setitem__(self, key, value):
raise NotImplementedError('Method is removed as we are not'
' able to determine '
'appropriate logic for it')
def __imul__(self, other):
t0 = len(self)
list.__imul__(self, other)
if self.parent is not None:
self.parent.extend(self[t0:])
class treedict(dict):
"""A dict that passes mutable extending operations used in Model
to parent dict instance.
Extending treedict you will also extend its parent
"""
def __init__(self, iterable=(), parent=None, **kwargs):
super().__init__(iterable, **kwargs)
assert isinstance(parent, dict) or parent is None
self.parent = parent
if self.parent is not None:
self.parent.update(self)
# typechecking here works bad
__setitem__ = withparent(dict.__setitem__)
update = withparent(dict.update)
def tree_contains(self, item):
# needed for `add_random_variable` method
if isinstance(self.parent, treedict):
return (dict.__contains__(self, item) or
self.parent.tree_contains(item))
elif isinstance(self.parent, dict):
return (dict.__contains__(self, item) or
self.parent.__contains__(item))
else:
return dict.__contains__(self, item)
class ValueGradFunction:
"""Create a theano function that computes a value and its gradient.
Parameters
----------
cost : theano variable
The value that we compute with its gradient.
grad_vars : list of named theano variables or None
The arguments with respect to which the gradient is computed.
extra_vars : list of named theano variables or None
Other arguments of the function that are assumed constant. They
are stored in shared variables and can be set using
`set_extra_values`.
dtype : str, default=theano.config.floatX
The dtype of the arrays.
casting : {'no', 'equiv', 'save', 'same_kind', 'unsafe'}, default='no'
Casting rule for casting `grad_args` to the array dtype.
See `numpy.can_cast` for a description of the options.
Keep in mind that we cast the variables to the array *and*
back from the array dtype to the variable dtype.
kwargs
Extra arguments are passed on to `theano.function`.
Attributes
----------
size : int
The number of elements in the parameter array.
profile : theano profiling object or None
The profiling object of the theano function that computes value and
gradient. This is None unless `profile=True` was set in the
kwargs.
"""
def __init__(self, cost, grad_vars, extra_vars=None, dtype=None,
casting='no', **kwargs):
from .distributions import TensorType
if extra_vars is None:
extra_vars = []
names = [arg.name for arg in grad_vars + extra_vars]
if any(name is None for name in names):
raise ValueError('Arguments must be named.')
if len(set(names)) != len(names):
raise ValueError('Names of the arguments are not unique.')
if cost.ndim > 0:
raise ValueError('Cost must be a scalar.')
self._grad_vars = grad_vars
self._extra_vars = extra_vars
self._extra_var_names = set(var.name for var in extra_vars)
self._cost = cost
self._ordering = ArrayOrdering(grad_vars)
self.size = self._ordering.size
self._extra_are_set = False
if dtype is None:
dtype = theano.config.floatX
self.dtype = dtype
for var in self._grad_vars:
if not np.can_cast(var.dtype, self.dtype, casting):
raise TypeError('Invalid dtype for variable %s. Can not '
'cast to %s with casting rule %s.'
% (var.name, self.dtype, casting))
if not np.issubdtype(var.dtype, np.floating):
raise TypeError('Invalid dtype for variable %s. Must be '
'floating point but is %s.'
% (var.name, var.dtype))
givens = []
self._extra_vars_shared = {}
for var in extra_vars:
shared = theano.shared(var.tag.test_value, var.name + '_shared__')
# test TensorType compatibility
if hasattr(var.tag.test_value, 'shape'):
testtype = TensorType(var.dtype, var.tag.test_value.shape)
if testtype != shared.type:
shared.type = testtype
self._extra_vars_shared[var.name] = shared
givens.append((var, shared))
self._vars_joined, self._cost_joined = self._build_joined(
self._cost, grad_vars, self._ordering.vmap)
grad = tt.grad(self._cost_joined, self._vars_joined)
grad.name = '__grad'
inputs = [self._vars_joined]
self._theano_function = theano.function(
inputs, [self._cost_joined, grad], givens=givens, **kwargs)
def set_extra_values(self, extra_vars):
self._extra_are_set = True
for var in self._extra_vars:
self._extra_vars_shared[var.name].set_value(extra_vars[var.name])
def get_extra_values(self):
if not self._extra_are_set:
raise ValueError('Extra values are not set.')
return {var.name: self._extra_vars_shared[var.name].get_value()
for var in self._extra_vars}
def __call__(self, array, grad_out=None, extra_vars=None):
if extra_vars is not None:
self.set_extra_values(extra_vars)
if not self._extra_are_set:
raise ValueError('Extra values are not set.')
if array.shape != (self.size,):
raise ValueError('Invalid shape for array. Must be %s but is %s.'
% ((self.size,), array.shape))
if grad_out is None:
out = np.empty_like(array)
else:
out = grad_out
logp, dlogp = self._theano_function(array)
if grad_out is None:
return logp, dlogp
else:
out[...] = dlogp
return logp
@property
def profile(self):
"""Profiling information of the underlying theano function."""
return self._theano_function.profile
def dict_to_array(self, point):
"""Convert a dictionary with values for grad_vars to an array."""
array = np.empty(self.size, dtype=self.dtype)
for varmap in self._ordering.vmap:
array[varmap.slc] = point[varmap.var].ravel().astype(self.dtype)
return array
def array_to_dict(self, array):
"""Convert an array to a dictionary containing the grad_vars."""
if array.shape != (self.size,):
raise ValueError('Array should have shape (%s,) but has %s'
% (self.size, array.shape))
if array.dtype != self.dtype:
raise ValueError('Array has invalid dtype. Should be %s but is %s'
% (self._dtype, self.dtype))
point = {}
for varmap in self._ordering.vmap:
data = array[varmap.slc].reshape(varmap.shp)
point[varmap.var] = data.astype(varmap.dtyp)
return point
def array_to_full_dict(self, array):
"""Convert an array to a dictionary with grad_vars and extra_vars."""
point = self.array_to_dict(array)
for name, var in self._extra_vars_shared.items():
point[name] = var.get_value()
return point
def _build_joined(self, cost, args, vmap):
args_joined = tt.vector('__args_joined')
args_joined.tag.test_value = np.zeros(self.size, dtype=self.dtype)
joined_slices = {}
for vmap in vmap:
sliced = args_joined[vmap.slc].reshape(vmap.shp)
sliced.name = vmap.var
joined_slices[vmap.var] = sliced
replace = {var: joined_slices[var.name] for var in args}
return args_joined, theano.clone(cost, replace=replace)
class Model(Context, Factor, WithMemoization, metaclass=InitContextMeta):
"""Encapsulates the variables and likelihood factors of a model.
Model class can be used for creating class based models. To create
a class based model you should inherit from :class:`~.Model` and
override :meth:`~.__init__` with arbitrary definitions (do not
forget to call base class :meth:`__init__` first).
Parameters
----------
name : str
name that will be used as prefix for names of all random
variables defined within model
model : Model
instance of Model that is supposed to be a parent for the new
instance. If ``None``, context will be used. All variables
defined within instance will be passed to the parent instance.
So that 'nested' model contributes to the variables and
likelihood factors of parent model.
theano_config : dict
A dictionary of theano config values that should be set
temporarily in the model context. See the documentation
of theano for a complete list. Set config key
``compute_test_value`` to `raise` if it is None.
Examples
--------
How to define a custom model
.. code-block:: python
class CustomModel(Model):
# 1) override init
def __init__(self, mean=0, sigma=1, name='', model=None):
# 2) call super's init first, passing model and name
# to it name will be prefix for all variables here if
# no name specified for model there will be no prefix
super().__init__(name, model)
# now you are in the context of instance,
# `modelcontext` will return self you can define
# variables in several ways note, that all variables
# will get model's name prefix
# 3) you can create variables with Var method
self.Var('v1', Normal.dist(mu=mean, sigma=sd))
# this will create variable named like '{prefix_}v1'
# and assign attribute 'v1' to instance created
# variable can be accessed with self.v1 or self['v1']
# 4) this syntax will also work as we are in the
# context of instance itself, names are given as usual
Normal('v2', mu=mean, sigma=sd)
# something more complex is allowed, too
half_cauchy = HalfCauchy('sd', beta=10, testval=1.)
Normal('v3', mu=mean, sigma=half_cauchy)
# Deterministic variables can be used in usual way
Deterministic('v3_sq', self.v3 ** 2)
# Potentials too
Potential('p1', tt.constant(1))
# After defining a class CustomModel you can use it in several
# ways
# I:
# state the model within a context
with Model() as model:
CustomModel()
# arbitrary actions
# II:
# use new class as entering point in context
with CustomModel() as model:
Normal('new_normal_var', mu=1, sigma=0)
# III:
# just get model instance with all that was defined in it
model = CustomModel()
# IV:
# use many custom models within one context
with Model() as model:
CustomModel(mean=1, name='first')
CustomModel(mean=2, name='second')
"""
def __new__(cls, *args, **kwargs):
# resolves the parent instance
instance = super().__new__(cls)
if kwargs.get('model') is not None:
instance._parent = kwargs.get('model')
elif cls.get_contexts():
instance._parent = cls.get_contexts()[-1]
else:
instance._parent = None
theano_config = kwargs.get('theano_config', None)
if theano_config is None or 'compute_test_value' not in theano_config:
theano_config = {'compute_test_value': 'raise'}
instance._theano_config = theano_config
return instance
def __init__(self, name='', model=None, theano_config=None):
self.name = name
if self.parent is not None:
self.named_vars = treedict(parent=self.parent.named_vars)
self.free_RVs = treelist(parent=self.parent.free_RVs)
self.observed_RVs = treelist(parent=self.parent.observed_RVs)
self.deterministics = treelist(parent=self.parent.deterministics)
self.potentials = treelist(parent=self.parent.potentials)
self.missing_values = treelist(parent=self.parent.missing_values)
else:
self.named_vars = treedict()
self.free_RVs = treelist()
self.observed_RVs = treelist()
self.deterministics = treelist()
self.potentials = treelist()
self.missing_values = treelist()
@property
def model(self):
return self
@property
def parent(self):
return self._parent
@property
def root(self):
model = self
while not model.isroot:
model = model.parent
return model
@property
def isroot(self):
return self.parent is None
@property
@memoize(bound=True)
def bijection(self):
vars = inputvars(self.vars)
bij = DictToArrayBijection(ArrayOrdering(vars),
self.test_point)
return bij
@property
def dict_to_array(self):
return self.bijection.map
@property
def ndim(self):
return sum(var.dsize for var in self.free_RVs)
@property
def logp_array(self):
return self.bijection.mapf(self.fastlogp)
@property
def dlogp_array(self):
vars = inputvars(self.cont_vars)
return self.bijection.mapf(self.fastdlogp(vars))
def logp_dlogp_function(self, grad_vars=None, **kwargs):
if grad_vars is None:
grad_vars = list(typefilter(self.free_RVs, continuous_types))
else:
for var in grad_vars:
if var.dtype not in continuous_types:
raise ValueError("Can only compute the gradient of "
"continuous types: %s" % var)
varnames = [var.name for var in grad_vars]
extra_vars = [var for var in self.free_RVs if var.name not in varnames]
return ValueGradFunction(self.logpt, grad_vars, extra_vars, **kwargs)
@property
def logpt(self):
"""Theano scalar of log-probability of the model"""
with self:
factors = [var.logpt for var in self.basic_RVs] + self.potentials
logp = tt.sum([tt.sum(factor) for factor in factors])
if self.name:
logp.name = '__logp_%s' % self.name
else:
logp.name = '__logp'
return logp
@property
def logp_nojact(self):
"""Theano scalar of log-probability of the model"""
with self:
factors = [var.logp_nojact for var in self.basic_RVs] + self.potentials
logp = tt.sum([tt.sum(factor) for factor in factors])
if self.name:
logp.name = '__logp_nojac_%s' % self.name
else:
logp.name = '__logp_nojac'
return logp
@property
def varlogpt(self):
"""Theano scalar of log-probability of the unobserved random variables
(excluding deterministic)."""
with self:
factors = [var.logpt for var in self.free_RVs]
return tt.sum(factors)
@property
def datalogpt(self):
with self:
factors = [var.logpt for var in self.observed_RVs]
factors += [tt.sum(factor) for factor in self.potentials]
return tt.sum(factors)
@property
def vars(self):
"""List of unobserved random variables used as inputs to the model
(which excludes deterministics).
"""
return self.free_RVs
@property
def basic_RVs(self):
"""List of random variables the model is defined in terms of
(which excludes deterministics).
"""
return self.free_RVs + self.observed_RVs
@property
def unobserved_RVs(self):
"""List of all random variable, including deterministic ones."""
return self.vars + self.deterministics
@property
def test_point(self):
"""Test point used to check that the model doesn't generate errors"""
return Point(((var, var.tag.test_value) for var in self.vars),
model=self)
@property
def disc_vars(self):
"""All the discrete variables in the model"""
return list(typefilter(self.vars, discrete_types))
@property
def cont_vars(self):
"""All the continuous variables in the model"""
return list(typefilter(self.vars, continuous_types))
def Var(self, name, dist, data=None, total_size=None):
"""Create and add (un)observed random variable to the model with an
appropriate prior distribution.
Parameters
----------
name : str
dist : distribution for the random variable
data : array_like (optional)
If data is provided, the variable is observed. If None,
the variable is unobserved.
total_size : scalar
upscales logp of variable with ``coef = total_size/var.shape[0]``
Returns
-------
FreeRV or ObservedRV
"""
name = self.name_for(name)
if data is None:
if getattr(dist, "transform", None) is None:
with self:
var = FreeRV(name=name, distribution=dist,
total_size=total_size, model=self)
self.free_RVs.append(var)
else:
with self:
var = TransformedRV(name=name, distribution=dist,
transform=dist.transform,
total_size=total_size,
model=self)
pm._log.debug('Applied {transform}-transform to {name}'
' and added transformed {orig_name} to model.'.format(
transform=dist.transform.name,
name=name,
orig_name=get_transformed_name(name, dist.transform)))
self.deterministics.append(var)
self.add_random_variable(var)
return var
elif isinstance(data, dict):
with self:
var = MultiObservedRV(name=name, data=data, distribution=dist,
total_size=total_size, model=self)
self.observed_RVs.append(var)
if var.missing_values:
self.free_RVs += var.missing_values
self.missing_values += var.missing_values
for v in var.missing_values:
self.named_vars[v.name] = v
else:
with self:
var = ObservedRV(name=name, data=data,
distribution=dist,
total_size=total_size, model=self)
self.observed_RVs.append(var)
if var.missing_values:
self.free_RVs.append(var.missing_values)
self.missing_values.append(var.missing_values)
self.named_vars[var.missing_values.name] = var.missing_values
self.add_random_variable(var)
return var
def add_random_variable(self, var):
"""Add a random variable to the named variables of the model."""
if self.named_vars.tree_contains(var.name):
raise ValueError(
"Variable name {} already exists.".format(var.name))
self.named_vars[var.name] = var
if not hasattr(self, self.name_of(var.name)):
setattr(self, self.name_of(var.name), var)
@property
def prefix(self):
return '%s_' % self.name if self.name else ''
def name_for(self, name):
"""Checks if name has prefix and adds if needed
"""
if self.prefix:
if not name.startswith(self.prefix):
return '{}{}'.format(self.prefix, name)
else:
return name
else:
return name
def name_of(self, name):
"""Checks if name has prefix and deletes if needed
"""
if not self.prefix or not name:
return name
elif name.startswith(self.prefix):
return name[len(self.prefix):]
else:
return name
def __getitem__(self, key):
try:
return self.named_vars[key]
except KeyError as e:
try:
return self.named_vars[self.name_for(key)]
except KeyError:
raise e
def makefn(self, outs, mode=None, *args, **kwargs):
"""Compiles a Theano function which returns ``outs`` and takes the variable
ancestors of ``outs`` as inputs.
Parameters
----------
outs : Theano variable or iterable of Theano variables
mode : Theano compilation mode
Returns
-------
Compiled Theano function
"""
with self:
return theano.function(self.vars, outs,
allow_input_downcast=True,
on_unused_input='ignore',
accept_inplace=True,
mode=mode, *args, **kwargs)
def fn(self, outs, mode=None, *args, **kwargs):
"""Compiles a Theano function which returns the values of ``outs``
and takes values of model vars as arguments.
Parameters
----------
outs : Theano variable or iterable of Theano variables
mode : Theano compilation mode
Returns
-------
Compiled Theano function
"""
return LoosePointFunc(self.makefn(outs, mode, *args, **kwargs), self)
def fastfn(self, outs, mode=None, *args, **kwargs):
"""Compiles a Theano function which returns ``outs`` and takes values
of model vars as a dict as an argument.
Parameters
----------
outs : Theano variable or iterable of Theano variables
mode : Theano compilation mode
Returns
-------
Compiled Theano function as point function.
"""
f = self.makefn(outs, mode, *args, **kwargs)
return FastPointFunc(f)
def profile(self, outs, n=1000, point=None, profile=True, *args, **kwargs):
"""Compiles and profiles a Theano function which returns ``outs`` and
takes values of model vars as a dict as an argument.
Parameters
----------
outs : Theano variable or iterable of Theano variables
n : int, default 1000
Number of iterations to run
point : point
Point to pass to the function
profile : True or ProfileStats
args, kwargs
Compilation args
Returns
-------
ProfileStats
Use .summary() to print stats.
"""
f = self.makefn(outs, profile=profile, *args, **kwargs)
if point is None:
point = self.test_point
for _ in range(n):
f(**point)
return f.profile
def flatten(self, vars=None, order=None, inputvar=None):
"""Flattens model's input and returns:
FlatView with
* input vector variable
* replacements ``input_var -> vars``
* view `{variable: VarMap}`
Parameters
----------
vars : list of variables or None
if None, then all model.free_RVs are used for flattening input
order : ArrayOrdering
Optional, use predefined ordering
inputvar : tt.vector
Optional, use predefined inputvar
Returns
-------
flat_view
"""
if vars is None:
vars = self.free_RVs
if order is None:
order = ArrayOrdering(vars)
if inputvar is None:
inputvar = tt.vector('flat_view', dtype=theano.config.floatX)
if theano.config.compute_test_value != 'off':
if vars:
inputvar.tag.test_value = flatten_list(vars).tag.test_value
else:
inputvar.tag.test_value = np.asarray([], inputvar.dtype)
replacements = {self.named_vars[name]: inputvar[slc].reshape(shape).astype(dtype)
for name, slc, shape, dtype in order.vmap}
view = {vm.var: vm for vm in order.vmap}
flat_view = FlatView(inputvar, replacements, view)
return flat_view
def check_test_point(self, test_point=None, round_vals=2):
"""Checks log probability of test_point for all random variables in the model.
Parameters
----------
test_point : Point
Point to be evaluated.
if None, then all model.test_point is used
round_vals : int
Number of decimals to round log-probabilities
Returns
-------
Pandas Series
"""
if test_point is None:
test_point = self.test_point
return Series({RV.name:np.round(RV.logp(self.test_point), round_vals) for RV in self.basic_RVs},
name='Log-probability of test_point')
def _repr_latex_(self, name=None, dist=None):
tex_vars = []
for rv in itertools.chain(self.unobserved_RVs, self.observed_RVs):
rv_tex = rv.__latex__()
if rv_tex is not None:
array_rv = rv_tex.replace(r'\sim', r'&\sim &').strip('$')
tex_vars.append(array_rv)
return r'''$$
\begin{{array}}{{rcl}}
{}
\end{{array}}
$$'''.format('\\\\'.join(tex_vars))
__latex__ = _repr_latex_
def fn(outs, mode=None, model=None, *args, **kwargs):
"""Compiles a Theano function which returns the values of ``outs`` and
takes values of model vars as arguments.
Parameters
----------
outs : Theano variable or iterable of Theano variables
mode : Theano compilation mode
Returns
-------
Compiled Theano function
"""
model = modelcontext(model)
return model.fn(outs, mode, *args, **kwargs)
def fastfn(outs, mode=None, model=None):
"""Compiles a Theano function which returns ``outs`` and takes values of model
vars as a dict as an argument.
Parameters
----------
outs : Theano variable or iterable of Theano variables
mode : Theano compilation mode
Returns
-------
Compiled Theano function as point function.
"""
model = modelcontext(model)
return model.fastfn(outs, mode)
def Point(*args, **kwargs):
"""Build a point. Uses same args as dict() does.
Filters out variables not in the model. All keys are strings.
Parameters
----------
args, kwargs
arguments to build a dict
"""
model = modelcontext(kwargs.pop('model', None))
args = list(args)
try:
d = dict(*args, **kwargs)
except Exception as e:
raise TypeError(
"can't turn {} and {} into a dict. {}".format(args, kwargs, e))
return dict((str(k), np.array(v)) for k, v in d.items()
if str(k) in map(str, model.vars))
class FastPointFunc:
"""Wraps so a function so it takes a dict of arguments instead of arguments."""
def __init__(self, f):
self.f = f
def __call__(self, state):
return self.f(**state)
class LoosePointFunc:
"""Wraps so a function so it takes a dict of arguments instead of arguments
but can still take arguments."""
def __init__(self, f, model):
self.f = f
self.model = model
def __call__(self, *args, **kwargs):
point = Point(model=self.model, *args, **kwargs)
return self.f(**point)
compilef = fastfn
def _get_scaling(total_size, shape, ndim):
"""
Gets scaling constant for logp
Parameters
----------
total_size : int or list[int]
shape : shape
shape to scale
ndim : int
ndim hint
Returns
-------
scalar
"""
if total_size is None:
coef = floatX(1)
elif isinstance(total_size, int):
if ndim >= 1:
denom = shape[0]
else:
denom = 1
coef = floatX(total_size) / floatX(denom)
elif isinstance(total_size, (list, tuple)):
if not all(isinstance(i, int) for i in total_size if (i is not Ellipsis and i is not None)):
raise TypeError('Unrecognized `total_size` type, expected '
'int or list of ints, got %r' % total_size)
if Ellipsis in total_size:
sep = total_size.index(Ellipsis)
begin = total_size[:sep]
end = total_size[sep+1:]
if Ellipsis in end:
raise ValueError('Double Ellipsis in `total_size` is restricted, got %r' % total_size)
else:
begin = total_size
end = []
if (len(begin) + len(end)) > ndim:
raise ValueError('Length of `total_size` is too big, '
'number of scalings is bigger that ndim, got %r' % total_size)
elif (len(begin) + len(end)) == 0:
return floatX(1)
if len(end) > 0:
shp_end = shape[-len(end):]
else:
shp_end = np.asarray([])
shp_begin = shape[:len(begin)]
begin_coef = [floatX(t) / shp_begin[i] for i, t in enumerate(begin) if t is not None]
end_coef = [floatX(t) / shp_end[i] for i, t in enumerate(end) if t is not None]
coefs = begin_coef + end_coef
coef = tt.prod(coefs)
else:
raise TypeError('Unrecognized `total_size` type, expected '
'int or list of ints, got %r' % total_size)
return tt.as_tensor(floatX(coef))
class FreeRV(Factor, TensorVariable):
"""Unobserved random variable that a model is specified in terms of."""
def __init__(self, type=None, owner=None, index=None, name=None,
distribution=None, total_size=None, model=None):
"""
Parameters
----------
type : theano type (optional)
owner : theano owner (optional)
name : str
distribution : Distribution
model : Model
total_size : scalar Tensor (optional)
needed for upscaling logp
"""
if type is None:
type = distribution.type
super().__init__(type, owner, index, name)
if distribution is not None:
self.dshape = tuple(distribution.shape)
self.dsize = int(np.prod(distribution.shape))
self.distribution = distribution
self.tag.test_value = np.ones(
distribution.shape, distribution.dtype) * distribution.default()
self.logp_elemwiset = distribution.logp(self)
# The logp might need scaling in minibatches.
# This is done in `Factor`.
self.logp_sum_unscaledt = distribution.logp_sum(self)
self.logp_nojac_unscaledt = distribution.logp_nojac(self)
self.total_size = total_size
self.model = model
self.scaling = _get_scaling(total_size, self.shape, self.ndim)
incorporate_methods(source=distribution, destination=self,
methods=['random'],
wrapper=InstanceMethod)
def _repr_latex_(self, name=None, dist=None):
if self.distribution is None:
return None
if name is None:
name = self.name
if dist is None:
dist = self.distribution
return self.distribution._repr_latex_(name=name, dist=dist)
__latex__ = _repr_latex_
@property
def init_value(self):
"""Convenience attribute to return tag.test_value"""
return self.tag.test_value
def pandas_to_array(data):
if hasattr(data, 'values'): # pandas
if data.isnull().any().any(): # missing values
ret = np.ma.MaskedArray(data.values, data.isnull().values)
else:
ret = data.values
elif hasattr(data, 'mask'):
ret = data
elif isinstance(data, theano.gof.graph.Variable):
ret = data
elif sps.issparse(data):
ret = data
elif isgenerator(data):
ret = generator(data)
else:
ret = np.asarray(data)
return pm.floatX(ret)
def as_tensor(data, name, model, distribution):
dtype = distribution.dtype
data = pandas_to_array(data).astype(dtype)
if hasattr(data, 'mask'):
impute_message = ('Data in {name} contains missing values and'
' will be automatically imputed from the'
' sampling distribution.'.format(name=name))
warnings.warn(impute_message, UserWarning)
from .distributions import NoDistribution
testval = np.broadcast_to(distribution.default(), data.shape)[data.mask]
fakedist = NoDistribution.dist(shape=data.mask.sum(), dtype=dtype,
testval=testval, parent_dist=distribution)
missing_values = FreeRV(name=name + '_missing', distribution=fakedist,
model=model)
constant = tt.as_tensor_variable(data.filled())
dataTensor = tt.set_subtensor(
constant[data.mask.nonzero()], missing_values)
dataTensor.missing_values = missing_values
return dataTensor
elif sps.issparse(data):
data = sparse.basic.as_sparse(data, name=name)
data.missing_values = None
return data
else:
data = tt.as_tensor_variable(data, name=name)
data.missing_values = None
return data
class ObservedRV(Factor, TensorVariable):
"""Observed random variable that a model is specified in terms of.
Potentially partially observed.
"""
def __init__(self, type=None, owner=None, index=None, name=None, data=None,
distribution=None, total_size=None, model=None):
"""
Parameters
----------
type : theano type (optional)
owner : theano owner (optional)
name : str
distribution : Distribution
model : Model
total_size : scalar Tensor (optional)
needed for upscaling logp
"""
from .distributions import TensorType
if hasattr(data, 'type') and isinstance(data.type, tt.TensorType):
type = data.type
if type is None:
data = pandas_to_array(data)
type = TensorType(distribution.dtype, data.shape)
self.observations = data
super().__init__(type, owner, index, name)
if distribution is not None:
data = as_tensor(data, name, model, distribution)
self.missing_values = data.missing_values
self.logp_elemwiset = distribution.logp(data)
# The logp might need scaling in minibatches.
# This is done in `Factor`.
self.logp_sum_unscaledt = distribution.logp_sum(data)
self.logp_nojac_unscaledt = distribution.logp_nojac(data)
self.total_size = total_size
self.model = model
self.distribution = distribution
# make this RV a view on the combined missing/nonmissing array
theano.gof.Apply(theano.compile.view_op,
inputs=[data], outputs=[self])
self.tag.test_value = theano.compile.view_op(data).tag.test_value
self.scaling = _get_scaling(total_size, data.shape, data.ndim)
def _repr_latex_(self, name=None, dist=None):
if self.distribution is None:
return None
if name is None:
name = self.name
if dist is None:
dist = self.distribution
return self.distribution._repr_latex_(name=name, dist=dist)
__latex__ = _repr_latex_
@property
def init_value(self):
"""Convenience attribute to return tag.test_value"""
return self.tag.test_value
class MultiObservedRV(Factor):
"""Observed random variable that a model is specified in terms of.
Potentially partially observed.
"""
def __init__(self, name, data, distribution, total_size=None, model=None):
"""
Parameters
----------
type : theano type (optional)
owner : theano owner (optional)
name : str
distribution : Distribution
model : Model
total_size : scalar Tensor (optional)
needed for upscaling logp
"""
self.name = name
self.data = {name: as_tensor(data, name, model, distribution)
for name, data in data.items()}
self.missing_values = [datum.missing_values for datum in self.data.values()
if datum.missing_values is not None]
self.logp_elemwiset = distribution.logp(**self.data)
# The logp might need scaling in minibatches.
# This is done in `Factor`.
self.logp_sum_unscaledt = distribution.logp_sum(**self.data)
self.logp_nojac_unscaledt = distribution.logp_nojac(**self.data)
self.total_size = total_size
self.model = model
self.distribution = distribution
self.scaling = _get_scaling(total_size, self.logp_elemwiset.shape, self.logp_elemwiset.ndim)
# Make hashable by id for draw_values
def __hash__(self):
return id(self)
def __eq__(self, other):
return self.id == other.id
def __ne__(self, other):
return not self == other
def _walk_up_rv(rv):
"""Walk up theano graph to get inputs for deterministic RV."""
all_rvs = []
parents = list(itertools.chain(*[j.inputs for j in rv.get_parents()]))
if parents:
for parent in parents:
all_rvs.extend(_walk_up_rv(parent))
else:
if rv.name:
all_rvs.append(r'\text{%s}' % rv.name)
else:
all_rvs.append(r'\text{Constant}')
return all_rvs
def _latex_repr_rv(rv):
"""Make latex string for a Deterministic variable"""
return r'$\text{%s} \sim \text{Deterministic}(%s)$' % (rv.name, r',~'.join(_walk_up_rv(rv)))
def Deterministic(name, var, model=None):
"""Create a named deterministic variable
Parameters
----------
name : str
var : theano variables
Returns
-------
var : var, with name attribute
"""
model = modelcontext(model)
var = var.copy(model.name_for(name))
model.deterministics.append(var)
model.add_random_variable(var)
var._repr_latex_ = functools.partial(_latex_repr_rv, var)
var.__latex__ = var._repr_latex_
return var
def Potential(name, var, model=None):
"""Add an arbitrary factor potential to the model likelihood
Parameters
----------
name : str
var : theano variables
Returns
-------
var : var, with name attribute
"""
model = modelcontext(model)
var.name = model.name_for(name)
model.potentials.append(var)
model.add_random_variable(var)
return var
class TransformedRV(TensorVariable):
"""
Parameters
----------
type : theano type (optional)
owner : theano owner (optional)
name : str
distribution : Distribution
model : Model
total_size : scalar Tensor (optional)
needed for upscaling logp
"""
def __init__(self, type=None, owner=None, index=None, name=None,
distribution=None, model=None, transform=None,
total_size=None):
if type is None:
type = distribution.type
super().__init__(type, owner, index, name)
self.transformation = transform
if distribution is not None:
self.model = model
self.distribution = distribution
self.dshape = tuple(distribution.shape)
self.dsize = int(np.prod(distribution.shape))
transformed_name = get_transformed_name(name, transform)
self.transformed = model.Var(
transformed_name, transform.apply(distribution), total_size=total_size)
normalRV = transform.backward(self.transformed)
theano.Apply(theano.compile.view_op, inputs=[
normalRV], outputs=[self])
self.tag.test_value = normalRV.tag.test_value
self.scaling = _get_scaling(total_size, self.shape, self.ndim)
incorporate_methods(source=distribution, destination=self,
methods=['random'],
wrapper=InstanceMethod)
def _repr_latex_(self, name=None, dist=None):
if self.distribution is None:
return None
if name is None:
name = self.name
if dist is None:
dist = self.distribution
return self.distribution._repr_latex_(name=name, dist=dist)
__latex__ = _repr_latex_
@property
def init_value(self):
"""Convenience attribute to return tag.test_value"""
return self.tag.test_value
def as_iterargs(data):
if isinstance(data, tuple):
return data
else:
return [data]
def all_continuous(vars):
"""Check that vars not include discrete variables, excepting
ObservedRVs. """
vars_ = [var for var in vars if not isinstance(var, pm.model.ObservedRV)]
if any([var.dtype in pm.discrete_types for var in vars_]):
return False
else:
return True