def test_get_assertions(self):
self.Independencies1 = Independencies(["X", "Y", "Z"])
self.assertEqual(self.Independencies1.independencies,
self.Independencies1.get_assertions())
self.Independencies2 = Independencies(["A", "B", "C"], ["D", "E", "F"])
self.assertEqual(self.Independencies2.independencies,
self.Independencies2.get_assertions())
def local_independencies(self, variables):
"""
Returns an instance of Independencies containing the local independencies
of each of the variables.
Parameters
----------
variables: str or array like
variables whose local independencies are to found.
Examples
--------
>>> from pgmpy.models import NaiveBayes
>>> model = NaiveBayes()
>>> model.add_edges_from([('a', 'b'), ('a', 'c'), ('a', 'd')])
>>> ind = model.local_independencies('b')
>>> ind
(b _|_ d, c | a)
"""
independencies = Independencies()
for variable in [variables] if isinstance(variables,
str) else variables:
if variable != self.parent_node:
independencies.add_assertions([
variable,
list(set(self.children_nodes) - set(variable)),
self.parent_node
])
return independencies
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 pgmpy.factors 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 test_get_independencies(self):
chain = BayesianModel([('X', 'Y'), ('Y', 'Z')])
self.assertEqual(chain.get_independencies(), Independencies(('X', 'Z', 'Y'), ('Z', 'X', 'Y')))
fork = BayesianModel([('Y', 'X'), ('Y', 'Z')])
self.assertEqual(fork.get_independencies(), Independencies(('X', 'Z', 'Y'), ('Z', 'X', 'Y')))
collider = BayesianModel([('X', 'Y'), ('Z', 'Y')])
self.assertEqual(collider.get_independencies(), Independencies(('X', 'Z'), ('Z', 'X')))
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
--------
>>> from pgmpy.factors import JointProbabilityDistribution
>>> prob = JointProbabilityDistribution(['x1', 'x2', 'x3'], [2, 3, 2], np.ones(8)/8)
>>> prob.get_independencies()
"""
if condition:
self.conditional_distribution(condition)
independencies = Independencies()
from itertools import combinations
for variable_pair in combinations(list(self.variables), 2):
from copy import deepcopy
if JointProbabilityDistribution.marginal_distribution(deepcopy(self), variable_pair) == \
JointProbabilityDistribution.marginal_distribution(deepcopy(self), variable_pair[0]) * \
JointProbabilityDistribution.marginal_distribution(deepcopy(self), variable_pair[1]):
independencies.add_assertions(variable_pair)
return independencies
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 pgmpy.factors 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 test_get_assertions(self):
self.Independencies1 = Independencies(['X', 'Y', 'Z'])
self.assertEqual(self.Independencies1.independencies,
self.Independencies1.get_assertions())
self.Independencies2 = Independencies(['A', 'B', 'C'], ['D', 'E', 'F'])
self.assertEqual(self.Independencies2.independencies,
self.Independencies2.get_assertions())
def test_build_skeleton(self):
ind = Independencies(['B', 'C'], ['A', ['B', 'C'], 'D'])
ind = ind.closure()
skel1, sep_sets1 = ConstraintBasedEstimator.build_skeleton("ABCD", ind)
self.assertTrue(
self._edge_list_equal(skel1.edges(), [('A', 'D'), ('B', 'D'),
('C', 'D')]))
sep_sets_ref1 = {
frozenset({'A', 'C'}): (),
frozenset({'A', 'B'}): (),
frozenset({'C', 'B'}): ()
}
self.assertEqual(sep_sets1, sep_sets_ref1)
model = BayesianModel([('A', 'C'), ('B', 'C'), ('B', 'D'), ('C', 'E')])
skel2, sep_sets2 = ConstraintBasedEstimator.build_skeleton(
model.nodes(), model.get_independencies())
self.assertTrue(
self._edge_list_equal(skel2, [('D', 'B'), ('A', 'C'), ('B', 'C'),
('C', 'E')]))
sep_sets_ref2 = {
frozenset({'D', 'C'}): ('B', ),
frozenset({'E', 'B'}): ('C', ),
frozenset({'A', 'D'}): (),
frozenset({'E', 'D'}): ('C', ),
frozenset({'E', 'A'}): ('C', ),
frozenset({'A', 'B'}): ()
}
# witnesses/seperators might change on each run, so we cannot compare directly
self.assertEqual(sep_sets2.keys(), sep_sets_ref2.keys())
self.assertEqual([len(v) for v in sorted(sep_sets2.values())],
[len(v) for v in sorted(sep_sets_ref2.values())])
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
--------
>>> from pgmpy.factors import JointProbabilityDistribution
>>> prob = JointProbabilityDistribution(['x1', 'x2', 'x3'], [2, 3, 2], np.ones(8)/8)
>>> prob.get_independencies()
"""
if condition:
self.conditional_distribution(condition)
independencies = Independencies()
from itertools import combinations
for variable_pair in combinations(list(self.variables), 2):
from copy import deepcopy
if JointProbabilityDistribution.marginal_distribution(deepcopy(self), variable_pair) == \
JointProbabilityDistribution.marginal_distribution(deepcopy(self), variable_pair[0]) * \
JointProbabilityDistribution.marginal_distribution(deepcopy(self), variable_pair[1]):
independencies.add_assertions(variable_pair)
return independencies
def test_get_independencies(self):
independencies = Independencies(['x1', 'x2'], ['x2', 'x3'], ['x3', 'x1'])
independencies1 = Independencies(['x1', 'x2'])
self.assertEqual(self.jpd1.get_independencies(), independencies)
self.assertEqual(self.jpd2.get_independencies(), independencies1)
self.assertEqual(self.jpd1.get_independencies([('x3', 0)]), independencies1)
self.assertEqual(self.jpd2.get_independencies([('x3', 0)]), Independencies())
def local_independencies(self, variables):
"""
Returns an instance of Independencies containing the local independencies
of each of the variables.
Parameters
----------
variables: str or array like
variables whose local independencies are to found.
Examples
--------
>>> from pgmpy.models import NaiveBayes
>>> model = NaiveBayes()
>>> model.add_edges_from([('a', 'b'), ('a', 'c'), ('a', 'd')])
>>> ind = model.local_independencies('b')
>>> ind
(b _|_ d, c | a)
"""
independencies = Independencies()
for variable in [variables] if isinstance(variables, str) else variables:
if variable != self.parent_node:
independencies.add_assertions([variable, list(set(self.children_nodes) - set(variable)), self.parent_node])
return independencies
def test_local_independencies(self):
self.assertEqual(self.G1.local_independencies('a'), Independencies())
self.assertEqual(self.G1.local_independencies('b'),
Independencies(['b', ['e', 'c', 'd'], 'a']))
self.assertEqual(self.G1.local_independencies('c'),
Independencies(['c', ['e', 'b', 'd'], 'a']))
self.assertEqual(self.G1.local_independencies('d'),
Independencies(['d', ['b', 'c', 'e'], 'a']))
def test_local_independencies(self):
self.assertListEqual(self.G1.local_independencies('a'), [None])
self.assertListEqual(self.G1.local_independencies('b'),
[Independencies(['b', ['e', 'c', 'd'], 'a'])])
self.assertListEqual(self.G1.local_independencies('c'),
[Independencies(['c', ['e', 'b', 'd'], 'a'])])
self.assertListEqual(self.G1.local_independencies('d'),
[Independencies(['d', ['b', 'c', 'e'], 'a'])])
def test_get_independencies(self):
chain = BayesianModel([("X", "Y"), ("Y", "Z")])
self.assertEqual(chain.get_independencies(),
Independencies(("X", "Z", "Y"), ("Z", "X", "Y")))
fork = BayesianModel([("Y", "X"), ("Y", "Z")])
self.assertEqual(fork.get_independencies(),
Independencies(("X", "Z", "Y"), ("Z", "X", "Y")))
collider = BayesianModel([("X", "Y"), ("Z", "Y")])
self.assertEqual(collider.get_independencies(),
Independencies(("X", "Z"), ("Z", "X")))
def setUp(self):
self.Independencies = Independencies()
self.Independencies3 = Independencies(
["a", ["b", "c", "d"], ["e", "f", "g"]],
["c", ["d", "e", "f"], ["g", "h"]])
self.Independencies4 = Independencies(
[["f", "d", "e"], "c", ["h", "g"]],
[["b", "c", "d"], "a", ["f", "g", "e"]])
self.Independencies5 = Independencies(
["a", ["b", "c", "d"], ["e", "f", "g"]],
["c", ["d", "e", "f"], "g"])
def setUp(self):
self.Independencies = Independencies()
self.Independencies3 = Independencies(
['a', ['b', 'c', 'd'], ['e', 'f', 'g']],
['c', ['d', 'e', 'f'], ['g', 'h']])
self.Independencies4 = Independencies(
[['f', 'd', 'e'], 'c', ['h', 'g']],
[['b', 'c', 'd'], 'a', ['f', 'g', 'e']])
self.Independencies5 = Independencies(
['a', ['b', 'c', 'd'], ['e', 'f', 'g']],
['c', ['d', 'e', 'f'], 'g'])
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 found.
Examples
--------
>>> from pgmpy.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 there can't be any cycles in the Bayesian Network. This is a
very simple dfs which doen't 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
from pgmpy.independencies import Independencies
independencies = Independencies()
for variable in [variables] if isinstance(variables,
str) else variables:
independencies.add_assertions([
variable,
set(self.nodes()) - set(dfs(variable)) -
set(self.get_parents(variable)) - {variable},
set(self.get_parents(variable))
])
return independencies
def test_local_independencies(self):
self.assertEqual(self.G1.local_independencies("a"), Independencies())
self.assertEqual(
self.G1.local_independencies("b"),
Independencies(["b", ["e", "c", "d"], "a"]),
)
self.assertEqual(
self.G1.local_independencies("c"),
Independencies(["c", ["e", "b", "d"], "a"]),
)
self.assertEqual(
self.G1.local_independencies("d"),
Independencies(["d", ["b", "c", "e"], "a"]),
)
def test_estimate_from_independencies(self):
ind = Independencies(['B', 'C'], ['A', ['B', 'C'], 'D'])
ind = ind.closure()
model = ConstraintBasedEstimator.estimate_from_independencies("ABCD", ind)
self.assertSetEqual(set(model.edges()),
set([('B', 'D'), ('A', 'D'), ('C', 'D')]))
model1 = BayesianModel([('A', 'C'), ('B', 'C'), ('B', 'D'), ('C', 'E')])
model2 = ConstraintBasedEstimator.estimate_from_independencies(
model1.nodes(),
model1.get_independencies())
self.assertTrue(set(model2.edges()) == set(model1.edges()) or
set(model2.edges()) == set([('B', 'C'), ('A', 'C'), ('C', 'E'), ('D', 'B')]))
def test_entails(self):
ind1 = Independencies([['A', 'B'], ['C', 'D'], 'E'])
ind2 = Independencies(['A', 'C', 'E'])
self.assertTrue(ind1.entails(ind2))
self.assertFalse(ind2.entails(ind1))
ind3 = Independencies(('W', ['X', 'Y', 'Z']))
self.assertTrue(ind3.entails(ind3.closure()))
self.assertTrue(ind3.closure().entails(ind3))
def local_independencies(self, variables):
"""
Returns a list of independencies objects containing the local independencies
of each of the variables. If local independencies does not exist for a variable
it gives a None for that variable.
Parameters
----------
variables: str or array like
variables whose local independencies are to found.
Examples
--------
>>> from pgmpy.models import NaiveBayes
>>> model = NaiveBayes()
>>> model.add_edges_from([('a', 'b'), ('a', 'c'), ('a', 'd')])
>>> ind = model.local_independencies('b')
>>> ind
[(b _|_ d, c | a)]
"""
independencies = []
for variable in [variables] if isinstance(variables,
str) else variables:
if variable != self.parent_node:
independencies.append(
Independencies([
variable,
list(set(self.children_nodes) - set(variable)),
self.parent_node
]))
else:
independencies.append(None)
return independencies
def local_independencies(self, variables):
"""
Returns an instance of Independencies 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 pgmpy.models import BayesianModel
>>> student = BayesianModel()
>>> student.add_edges_from([('diff', 'grade'), ('intel', 'grade'),
>>> ('grade', 'letter'), ('intel', 'SAT')])
>>> ind = student.local_independencies('grade')
>>> ind
(grade _|_ SAT | 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,
(list,
tuple)) 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 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 found.
Examples
--------
>>> from pgmpy.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 there can't be any cycles in the Bayesian Network. This is a
very simple dfs which doen't 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
from pgmpy.independencies import Independencies
independencies = Independencies()
for variable in [variables] if isinstance(variables, str) else variables:
independencies.add_assertions([variable, set(self.nodes()) - set(dfs(variable)) -
set(self.get_parents(variable)) - {variable},
set(self.get_parents(variable))])
return independencies
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 pgmpy.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 test_estimate_from_independencies(self):
ind = Independencies(['B', 'C'], ['A', ['B', 'C'], 'D'])
ind = ind.closure()
model = ConstraintBasedEstimator.estimate_from_independencies(
"ABCD", ind)
self.assertSetEqual(set(model.edges()),
set([('B', 'D'), ('A', 'D'), ('C', 'D')]))
model1 = BayesianModel([('A', 'C'), ('B', 'C'), ('B', 'D'),
('C', 'E')])
model2 = ConstraintBasedEstimator.estimate_from_independencies(
model1.nodes(), model1.get_independencies())
self.assertTrue(
set(model2.edges()) == set(model1.edges())
or set(model2.edges()) == set([('B', 'C'), ('A', 'C'), ('C', 'E'),
('D', 'B')]))
def test_estimate_from_independencies(self):
ind = Independencies(["B", "C"], ["A", ["B", "C"], "D"])
ind = ind.closure()
model = ConstraintBasedEstimator.estimate_from_independencies(
"ABCD", ind)
self.assertSetEqual(set(model.edges()),
set([("B", "D"), ("A", "D"), ("C", "D")]))
model1 = BayesianModel([("A", "C"), ("B", "C"), ("B", "D"),
("C", "E")])
model2 = ConstraintBasedEstimator.estimate_from_independencies(
model1.nodes(), model1.get_independencies())
self.assertTrue(
set(model2.edges()) == set(model1.edges())
or set(model2.edges()) == set([("B", "C"), ("A", "C"), ("C", "E"),
("D", "B")]))
def local_independencies(self, variables):
"""
Returns an instance of Independencies 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 pgmpy.models import BayesianModel
>>> student = BayesianModel()
>>> student.add_edges_from([('diff', 'grade'), ('intel', 'grade'),
>>> ('grade', 'letter'), ('intel', 'SAT')])
>>> ind = student.local_independencies('grade')
>>> ind
(grade _|_ SAT | 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, (list, tuple)) 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_independencies(self, latex=False):
"""
Compute independencies in Bayesian Network.
Parameters
----------
latex: boolean
If latex=True then latex string of the independence assertion
would be created.
Examples
--------
>>> from pgmpy.models import BayesianModel
>>> student = BayesianModel()
>>> student.add_nodes_from(['diff', 'intel', 'grades', 'letter', 'sat'])
>>> student.add_edges_from([('diff', 'grades'), ('intel', 'grades'), ('grade', 'letter'),
... ('intel', 'sat')])
>>> student.get_independencies()
"""
independencies = Independencies()
for start in (self.nodes()):
for r in (1, len(self.nodes())):
for observed in itertools.combinations(self.nodes(), r):
independent_variables = self.active_trail_nodes(start, observed=observed)
independent_variables = set(independent_variables) - {start}
if independent_variables:
independencies.add_assertions([start, independent_variables,
observed])
independencies.reduce()
if not latex:
return independencies
else:
return independencies.latex_string()
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 pgmpy.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)[start])
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 test_is_equivalent(self):
ind1 = Independencies(["X", ["Y", "W"], "Z"])
ind2 = Independencies(["X", "Y", "Z"], ["X", "W", "Z"])
ind3 = Independencies(["X", "Y", "Z"], ["X", "W", "Z"],
["X", "Y", ["W", "Z"]])
self.assertFalse(ind1.is_equivalent(ind2))
self.assertTrue(ind1.is_equivalent(ind3))
def test_is_equivalent(self):
ind1 = Independencies(['X', ['Y', 'W'], 'Z'])
ind2 = Independencies(['X', 'Y', 'Z'], ['X', 'W', 'Z'])
ind3 = Independencies(['X', 'Y', 'Z'], ['X', 'W', 'Z'],
['X', 'Y', ['W', 'Z']])
self.assertFalse(ind1.is_equivalent(ind2))
self.assertTrue(ind1.is_equivalent(ind3))
def test_eq(self):
self.assertTrue(self.Independencies3 == self.Independencies4)
self.assertFalse(self.Independencies3 != self.Independencies4)
self.assertTrue(self.Independencies3 != self.Independencies5)
self.assertFalse(self.Independencies4 == self.Independencies5)
self.assertFalse(Independencies() == Independencies(["A", "B", "C"]))
self.assertFalse(Independencies(["A", "B", "C"]) == Independencies())
self.assertTrue(Independencies() == Independencies())
def test_eq(self):
self.assertTrue(self.Independencies3 == self.Independencies4)
self.assertFalse(self.Independencies3 != self.Independencies4)
self.assertTrue(self.Independencies3 != self.Independencies5)
self.assertFalse(self.Independencies4 == self.Independencies5)
self.assertFalse(Independencies() == Independencies(['A', 'B', 'C']))
self.assertFalse(Independencies(['A', 'B', 'C']) == Independencies())
self.assertTrue(Independencies() == Independencies())
def test_build_skeleton(self):
ind = Independencies(['B', 'C'], ['A', ['B', 'C'], 'D'])
ind = ind.closure()
skel1, sep_sets1 = ConstraintBasedEstimator.build_skeleton("ABCD", ind)
self.assertTrue(self._edge_list_equal(skel1.edges(), [('A', 'D'), ('B', 'D'), ('C', 'D')]))
sep_sets_ref1 = {frozenset({'A', 'C'}): (), frozenset({'A', 'B'}): (), frozenset({'C', 'B'}): ()}
self.assertEqual(sep_sets1, sep_sets_ref1)
model = BayesianModel([('A', 'C'), ('B', 'C'), ('B', 'D'), ('C', 'E')])
skel2, sep_sets2 = ConstraintBasedEstimator.build_skeleton(model.nodes(), model.get_independencies())
self.assertTrue(self._edge_list_equal(skel2, [('D', 'B'), ('A', 'C'), ('B', 'C'), ('C', 'E')]))
sep_sets_ref2 = {frozenset({'D', 'C'}): ('B',),
frozenset({'E', 'B'}): ('C',),
frozenset({'A', 'D'}): (),
frozenset({'E', 'D'}): ('C',),
frozenset({'E', 'A'}): ('C',),
frozenset({'A', 'B'}): ()}
# witnesses/seperators might change on each run, so we cannot compare directly
self.assertEqual(sep_sets2.keys(), sep_sets_ref2.keys())
self.assertEqual([len(v) for v in sorted(sep_sets2.values())],
[len(v) for v in sorted(sep_sets_ref2.values())])
def test_build_skeleton(self):
ind = Independencies(["B", "C"], ["A", ["B", "C"], "D"])
ind = ind.closure()
skel1, sep_sets1 = ConstraintBasedEstimator.build_skeleton("ABCD", ind)
self.assertTrue(
self._edge_list_equal(skel1.edges(), [("A", "D"), ("B", "D"),
("C", "D")]))
sep_sets_ref1 = {
frozenset({"A", "C"}): (),
frozenset({"A", "B"}): (),
frozenset({"C", "B"}): (),
}
self.assertEqual(sep_sets1, sep_sets_ref1)
model = BayesianModel([("A", "C"), ("B", "C"), ("B", "D"), ("C", "E")])
skel2, sep_sets2 = ConstraintBasedEstimator.build_skeleton(
model.nodes(), model.get_independencies())
self.assertTrue(
self._edge_list_equal(skel2, [("D", "B"), ("A", "C"), ("B", "C"),
("C", "E")]))
sep_sets_ref2 = {
frozenset({"D", "C"}): ("B", ),
frozenset({"E", "B"}): ("C", ),
frozenset({"A", "D"}): (),
frozenset({"E", "D"}): ("C", ),
frozenset({"E", "A"}): ("C", ),
frozenset({"A", "B"}): (),
}
# witnesses/seperators might change on each run, so we cannot compare directly
self.assertEqual(sep_sets2.keys(), sep_sets_ref2.keys())
self.assertEqual(
[len(v) for v in sorted(sep_sets2.values())],
[len(v) for v in sorted(sep_sets_ref2.values())],
)
def local_independencies(self, variables):
"""
Returns an instance of Independencies 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 pgmpy.models import DAG
>>> student = DAG()
>>> student.add_edges_from([('diff', 'grade'), ('intel', 'grade'),
>>> ('grade', 'letter'), ('intel', 'SAT')])
>>> ind = student.local_independencies('grade')
>>> ind
(grade _|_ SAT | diff, intel)
"""
independencies = Independencies()
for variable in (
variables if isinstance(variables, (list, tuple)) else [variables]
):
non_descendents = (
set(self.nodes())
- {variable}
- set(nx.dfs_preorder_nodes(self, 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 pgmpy.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()
"""
from pgmpy.exceptions import RequiredError
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 RequiredError:
pass
local_independencies.reduce()
if latex:
return local_independencies.latex_string()
else:
return local_independencies
def test_closure(self):
ind1 = Independencies(('A', ['B', 'C'], 'D'))
self.assertEqual(ind1.closure(), Independencies(('A', ['B', 'C'], 'D'),
('A', 'B', ['C', 'D']),
('A', 'C', ['B', 'D']),
('A', 'B', 'D'),
('A', 'C', 'D')))
ind2 = Independencies(('W', ['X', 'Y', 'Z']))
self.assertEqual(ind2.closure(),
Independencies(
('W', 'Y'), ('W', 'Y', 'X'), ('W', 'Y', 'Z'), ('W', 'Y', ['X', 'Z']),
('W', ['Y', 'X']), ('W', 'X', ['Y', 'Z']), ('W', ['X', 'Z'], 'Y'),
('W', 'X'), ('W', ['X', 'Z']), ('W', ['Y', 'Z'], 'X'),
('W', ['Y', 'X', 'Z']), ('W', 'X', 'Z'), ('W', ['Y', 'Z']),
('W', 'Z', 'X'), ('W', 'Z'), ('W', ['Y', 'X'], 'Z'), ('W', 'X', 'Y'),
('W', 'Z', ['Y', 'X']), ('W', 'Z', 'Y')))
ind3 = Independencies(('c', 'a', ['b', 'e', 'd']), (['e', 'c'], 'b', ['a', 'd']), (['b', 'd'], 'e', 'a'),
('e', ['b', 'd'], 'c'), ('e', ['b', 'c'], 'd'), (['e', 'c'], 'a', 'b'))
self.assertEqual(len(ind3.closure().get_assertions()), 78)
def get_independencies(self, latex=False):
"""
Compute independencies in Bayesian Network.
Parameters
----------
latex: boolean
If latex=True then latex string of the independence assertion
would be created.
Examples
--------
>>> from pgmpy.models import BayesianModel
>>> student = BayesianModel()
>>> student.add_nodes_from(['diff', 'intel', 'grades', 'letter', 'sat'])
>>> student.add_edges_from([('diff', 'grades'), ('intel', 'grades'), ('grade', 'letter'),
... ('intel', 'sat')])
>>> student.get_independencies()
"""
independencies = Independencies()
for start in (self.nodes()):
for r in (1, len(self.nodes())):
for observed in itertools.combinations(self.nodes(), r):
independent_variables = self.active_trail_nodes(
start, observed=observed)
independent_variables = set(independent_variables) - {
start
}
if independent_variables:
independencies.add_assertions(
[start, independent_variables, observed])
independencies.reduce()
if not latex:
return independencies
else:
return independencies.latex_string()
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 pgmpy.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()
"""
from pgmpy.exceptions import RequiredError
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 RequiredError:
pass
local_independencies.reduce()
if latex:
return local_independencies.latex_string()
else:
return local_independencies
def test_local_independencies(self):
self.graph.add_edges_from([('a', 'b'), ('b', 'c')])
independencies = self.graph.get_local_independencies()
self.assertIsInstance(independencies, Independencies)
self.assertEqual(independencies, Independencies(['a', 'c', 'b']))
def test_init(self):
self.Independencies1 = Independencies(['X', 'Y', 'Z'])
self.assertEqual(self.Independencies1, Independencies(['X', 'Y', 'Z']))
self.Independencies2 = Independencies()
self.assertEqual(self.Independencies2, Independencies())
def test_add_assertions(self):
self.Independencies1 = Independencies(['X', 'Y', 'Z'])
self.assertEqual(self.Independencies1, Independencies(['X', 'Y', 'Z']))
self.Independencies2 = Independencies(['A', 'B', 'C'], ['D', 'E', 'F'])
self.assertEqual(self.Independencies2, Independencies(['A', 'B', 'C'], ['D', 'E', 'F']))
def test_get_assertions(self):
self.Independencies1 = Independencies(['X', 'Y', 'Z'])
self.assertEqual(self.Independencies1.independencies, self.Independencies1.get_assertions())
self.Independencies2 = Independencies(['A', 'B', 'C'], ['D', 'E', 'F'])
self.assertEqual(self.Independencies2.independencies, self.Independencies2.get_assertions())
class TestIndependencies(unittest.TestCase):
def setUp(self):
self.Independencies = Independencies()
self.Independencies3 = Independencies(['a', ['b', 'c', 'd'], ['e', 'f', 'g']],
['c', ['d', 'e', 'f'], ['g', 'h']])
self.Independencies4 = Independencies([['f', 'd', 'e'], 'c', ['h', 'g']],
[['b', 'c', 'd'], 'a', ['f', 'g', 'e']])
self.Independencies5 = Independencies(['a', ['b', 'c', 'd'], ['e', 'f', 'g']],
['c', ['d', 'e', 'f'], 'g'])
def test_init(self):
self.Independencies1 = Independencies(['X', 'Y', 'Z'])
self.assertEqual(self.Independencies1, Independencies(['X', 'Y', 'Z']))
self.Independencies2 = Independencies()
self.assertEqual(self.Independencies2, Independencies())
def test_add_assertions(self):
self.Independencies1 = Independencies(['X', 'Y', 'Z'])
self.assertEqual(self.Independencies1, Independencies(['X', 'Y', 'Z']))
self.Independencies2 = Independencies(['A', 'B', 'C'], ['D', 'E', 'F'])
self.assertEqual(self.Independencies2, Independencies(['A', 'B', 'C'], ['D', 'E', 'F']))
def test_get_assertions(self):
self.Independencies1 = Independencies(['X', 'Y', 'Z'])
self.assertEqual(self.Independencies1.independencies, self.Independencies1.get_assertions())
self.Independencies2 = Independencies(['A', 'B', 'C'], ['D', 'E', 'F'])
self.assertEqual(self.Independencies2.independencies, self.Independencies2.get_assertions())
def test_closure(self):
ind1 = Independencies(('A', ['B', 'C'], 'D'))
self.assertEqual(ind1.closure(), Independencies(('A', ['B', 'C'], 'D'),
('A', 'B', ['C', 'D']),
('A', 'C', ['B', 'D']),
('A', 'B', 'D'),
('A', 'C', 'D')))
ind2 = Independencies(('W', ['X', 'Y', 'Z']))
self.assertEqual(ind2.closure(),
Independencies(
('W', 'Y'), ('W', 'Y', 'X'), ('W', 'Y', 'Z'), ('W', 'Y', ['X', 'Z']),
('W', ['Y', 'X']), ('W', 'X', ['Y', 'Z']), ('W', ['X', 'Z'], 'Y'),
('W', 'X'), ('W', ['X', 'Z']), ('W', ['Y', 'Z'], 'X'),
('W', ['Y', 'X', 'Z']), ('W', 'X', 'Z'), ('W', ['Y', 'Z']),
('W', 'Z', 'X'), ('W', 'Z'), ('W', ['Y', 'X'], 'Z'), ('W', 'X', 'Y'),
('W', 'Z', ['Y', 'X']), ('W', 'Z', 'Y')))
ind3 = Independencies(('c', 'a', ['b', 'e', 'd']), (['e', 'c'], 'b', ['a', 'd']), (['b', 'd'], 'e', 'a'),
('e', ['b', 'd'], 'c'), ('e', ['b', 'c'], 'd'), (['e', 'c'], 'a', 'b'))
self.assertEqual(len(ind3.closure().get_assertions()), 78)
def test_entails(self):
ind1 = Independencies([['A', 'B'], ['C', 'D'], 'E'])
ind2 = Independencies(['A', 'C', 'E'])
self.assertTrue(ind1.entails(ind2))
self.assertFalse(ind2.entails(ind1))
ind3 = Independencies(('W', ['X', 'Y', 'Z']))
self.assertTrue(ind3.entails(ind3.closure()))
self.assertTrue(ind3.closure().entails(ind3))
def test_is_equivalent(self):
ind1 = Independencies(['X', ['Y', 'W'], 'Z'])
ind2 = Independencies(['X', 'Y', 'Z'], ['X', 'W', 'Z'])
ind3 = Independencies(['X', 'Y', 'Z'], ['X', 'W', 'Z'], ['X', 'Y', ['W', 'Z']])
self.assertFalse(ind1.is_equivalent(ind2))
self.assertTrue(ind1.is_equivalent(ind3))
def test_eq(self):
self.assertTrue(self.Independencies3 == self.Independencies4)
self.assertFalse(self.Independencies3 != self.Independencies4)
self.assertTrue(self.Independencies3 != self.Independencies5)
self.assertFalse(self.Independencies4 == self.Independencies5)
self.assertFalse(Independencies() == Independencies(['A', 'B', 'C']))
self.assertFalse(Independencies(['A', 'B', 'C']) == Independencies())
self.assertTrue(Independencies() == Independencies())
def tearDown(self):
del self.Independencies
del self.Independencies3
del self.Independencies4
del self.Independencies5
def test_is_equivalent(self):
ind1 = Independencies(['X', ['Y', 'W'], 'Z'])
ind2 = Independencies(['X', 'Y', 'Z'], ['X', 'W', 'Z'])
ind3 = Independencies(['X', 'Y', 'Z'], ['X', 'W', 'Z'], ['X', 'Y', ['W', 'Z']])
self.assertFalse(ind1.is_equivalent(ind2))
self.assertTrue(ind1.is_equivalent(ind3))
def test_local_independencies(self):
self.graph.add_edges_from([("a", "b"), ("b", "c")])
independencies = self.graph.get_local_independencies()
self.assertIsInstance(independencies, Independencies)
self.assertEqual(independencies, Independencies(["a", "c", "b"]))
from pgmpy.independencies import Independencies # There are multiple ways to create an Independencies object, we # could either initialize an empty object or initialize with some # assertions. independencies = Independencies() # Empty object independencies.get_assertions() independencies.add_assertions(assertion1, assertion2) independencies.get_assertions()