def get_independencies(self, latex=False):
"""
Computes independencies in the Bayesian Network, by checking d-seperation.
Parameters
----------
latex: boolean
If latex=True then latex string of the independence assertion
would be created.
Examples
--------
>>> from pgm.models import BayesianModel
>>> chain = BayesianModel([('X', 'Y'), ('Y', 'Z')])
>>> chain.get_independencies()
(X _|_ Z | Y)
(Z _|_ X | Y)
"""
independencies = Independencies()
for start in (self.nodes()):
rest = set(self.nodes()) - {start}
for r in range(len(rest)):
for observed in itertools.combinations(rest, r):
d_seperated_variables = rest - set(observed) - set(
self.active_trail_nodes(start, observed=observed))
if d_seperated_variables:
independencies.add_assertions(
[start, d_seperated_variables, observed])
independencies.reduce()
if not latex:
return independencies
else:
return independencies.latex_string()
def get_independencies(self, condition=None):
"""
Returns the independent variables in the joint probability distribution.
Returns marginally independent variables if condition=None.
Returns conditionally independent variables if condition!=None
Parameter
---------
condition: array_like
Random Variable on which to condition the Joint Probability Distribution.
Examples
--------
>>> import numpy as np
>>> from pgm.factors.discrete import JointProbabilityDistribution
>>> prob = JointProbabilityDistribution(['x1', 'x2', 'x3'], [2, 3, 2], np.ones(12)/12)
>>> prob.get_independencies()
(x1 _|_ x2)
(x1 _|_ x3)
(x2 _|_ x3)
"""
JPD = self.copy()
if condition:
JPD.conditional_distribution(condition)
independencies = Independencies()
for variable_pair in itertools.combinations(list(JPD.variables), 2):
if (JPD.marginal_distribution(variable_pair, inplace=False) ==
JPD.marginal_distribution(variable_pair[0], inplace=False) *
JPD.marginal_distribution(variable_pair[1], inplace=False)):
independencies.add_assertions(variable_pair)
return independencies
def local_independencies(self, variables):
"""
Returns a independencies object containing the local independencies
of each of the variables.
Parameters
----------
variables: str or array like
variables whose local independencies are to be found.
Examples
--------
>>> from pgm.models import BayesianModel
>>> student = BayesianModel()
>>> student.add_edges_from([('diff', 'grade'), ('intel', 'grade'),
>>> ('grade', 'letter'), ('intel', 'SAT')])
>>> ind = student.local_independencies('grade')
>>> ind.event1
{'grade'}
>>> ind.event2
{'SAT'}
>>> ind.event3
{'diff', 'intel'}
"""
def dfs(node):
"""
Returns the descendents of node.
Since Bayesian Networks are acyclic, this is a very simple dfs
which does not remember which nodes it has visited.
"""
descendents = []
visit = [node]
while visit:
n = visit.pop()
neighbors = self.neighbors(n)
visit.extend(neighbors)
descendents.extend(neighbors)
return descendents
independencies = Independencies()
for variable in [variables] if isinstance(variables,
str) else variables:
non_descendents = set(self.nodes()) - {variable} - set(
dfs(variable))
parents = set(self.get_parents(variable))
if non_descendents - parents:
independencies.add_assertions(
[variable, non_descendents - parents, parents])
return independencies
def get_local_independencies(self, latex=False):
"""
Returns all the local independencies present in the markov model.
Local independencies are the independence assertion in the form of
.. math:: {X \perp W - {X} - MB(X) | MB(X)}
where MB is the markov blanket of all the random variables in X
Parameters
----------
latex: boolean
If latex=True then latex string of the indepedence assertion would
be created
Examples
--------
>>> from pgm.models import MarkovModel
>>> mm = MarkovModel()
>>> mm.add_nodes_from(['x1', 'x2', 'x3', 'x4', 'x5', 'x6', 'x7'])
>>> mm.add_edges_from([('x1', 'x3'), ('x1', 'x4'), ('x2', 'x4'),
... ('x2', 'x5'), ('x3', 'x6'), ('x4', 'x6'),
... ('x4', 'x7'), ('x5', 'x7')])
>>> mm.get_local_independecies()
"""
local_independencies = Independencies()
all_vars = set(self.nodes())
for node in self.nodes():
markov_blanket = set(self.markov_blanket(node))
rest = all_vars - set([node]) - markov_blanket
try:
local_independencies.add_assertions(
[node, list(rest), list(markov_blanket)])
except ValueError:
pass
local_independencies.reduce()
if latex:
return local_independencies.latex_string()
else:
return local_independencies