class TestUndirectedGraphCreation(unittest.TestCase):
def setUp(self):
self.graph = UndirectedGraph()
def test_class_init_without_data(self):
self.assertIsInstance(self.graph, UndirectedGraph)
def test_class_init_with_data_string(self):
self.G = UndirectedGraph([("a", "b"), ("b", "c")])
self.assertListEqual(sorted(self.G.nodes()), ["a", "b", "c"])
self.assertListEqual(hf.recursive_sorted(self.G.edges()), [["a", "b"], ["b", "c"]])
def test_add_node_string(self):
self.graph.add_node("a")
self.assertListEqual(self.graph.nodes(), ["a"])
def test_add_node_nonstring(self):
self.graph.add_node(1)
self.assertListEqual(self.graph.nodes(), [1])
def test_add_nodes_from_string(self):
self.graph.add_nodes_from(["a", "b", "c", "d"])
self.assertListEqual(sorted(self.graph.nodes()), ["a", "b", "c", "d"])
def test_add_nodes_from_non_string(self):
self.graph.add_nodes_from([1, 2, 3, 4])
def test_add_edge_string(self):
self.graph.add_edge("d", "e")
self.assertListEqual(sorted(self.graph.nodes()), ["d", "e"])
self.assertListEqual(hf.recursive_sorted(self.graph.edges()), [["d", "e"]])
self.graph.add_nodes_from(["a", "b", "c"])
self.graph.add_edge("a", "b")
self.assertListEqual(hf.recursive_sorted(self.graph.edges()), [["a", "b"], ["d", "e"]])
def test_add_edge_nonstring(self):
self.graph.add_edge(1, 2)
def test_add_edges_from_string(self):
self.graph.add_edges_from([("a", "b"), ("b", "c")])
self.assertListEqual(sorted(self.graph.nodes()), ["a", "b", "c"])
self.assertListEqual(hf.recursive_sorted(self.graph.edges()), [["a", "b"], ["b", "c"]])
self.graph.add_nodes_from(["d", "e", "f"])
self.graph.add_edges_from([("d", "e"), ("e", "f")])
self.assertListEqual(sorted(self.graph.nodes()), ["a", "b", "c", "d", "e", "f"])
self.assertListEqual(
hf.recursive_sorted(self.graph.edges()),
hf.recursive_sorted([("a", "b"), ("b", "c"), ("d", "e"), ("e", "f")]),
)
def test_add_edges_from_nonstring(self):
self.graph.add_edges_from([(1, 2), (2, 3)])
def test_number_of_neighbors(self):
self.graph.add_edges_from([("a", "b"), ("b", "c")])
self.assertEqual(len(self.graph.neighbors("b")), 2)
def tearDown(self):
del self.graph
class TestUndirectedGraphCreation(unittest.TestCase):
def setUp(self):
self.graph = UndirectedGraph()
def test_class_init_without_data(self):
self.assertIsInstance(self.graph, UndirectedGraph)
def test_class_init_with_data_string(self):
self.G = UndirectedGraph([('a', 'b'), ('b', 'c')])
self.assertListEqual(sorted(self.G.nodes()), ['a', 'b', 'c'])
self.assertListEqual(hf.recursive_sorted(self.G.edges()),
[['a', 'b'], ['b', 'c']])
def test_add_node_string(self):
self.graph.add_node('a')
self.assertListEqual(self.graph.nodes(), ['a'])
def test_add_node_nonstring(self):
self.graph.add_node(1)
self.assertListEqual(self.graph.nodes(), [1])
def test_add_nodes_from_string(self):
self.graph.add_nodes_from(['a', 'b', 'c', 'd'])
self.assertListEqual(sorted(self.graph.nodes()),
['a', 'b', 'c', 'd'])
def test_add_node_with_weight(self):
self.graph.add_node('a')
self.graph.add_node('weight_a', weight=0.3)
self.assertEqual(self.graph.node['weight_a']['weight'], 0.3)
self.assertEqual(self.graph.node['a']['weight'], None)
def test_add_nodes_from_with_weight(self):
self.graph.add_node(1)
self.graph.add_nodes_from(['weight_b', 'weight_c'], weights=[0.3, 0.5])
self.assertEqual(self.graph.node['weight_b']['weight'], 0.3)
self.assertEqual(self.graph.node['weight_c']['weight'], 0.5)
self.assertEqual(self.graph.node[1]['weight'], None)
def test_add_nodes_from_non_string(self):
self.graph.add_nodes_from([1, 2, 3, 4])
def test_add_edge_string(self):
self.graph.add_edge('d', 'e')
self.assertListEqual(sorted(self.graph.nodes()), ['d', 'e'])
self.assertListEqual(hf.recursive_sorted(self.graph.edges()),
[['d', 'e']])
self.graph.add_nodes_from(['a', 'b', 'c'])
self.graph.add_edge('a', 'b')
self.assertListEqual(hf.recursive_sorted(self.graph.edges()),
[['a', 'b'], ['d', 'e']])
def test_add_edge_nonstring(self):
self.graph.add_edge(1, 2)
def test_add_edges_from_string(self):
self.graph.add_edges_from([('a', 'b'), ('b', 'c')])
self.assertListEqual(sorted(self.graph.nodes()), ['a', 'b', 'c'])
self.assertListEqual(hf.recursive_sorted(self.graph.edges()),
[['a', 'b'], ['b', 'c']])
self.graph.add_nodes_from(['d', 'e', 'f'])
self.graph.add_edges_from([('d', 'e'), ('e', 'f')])
self.assertListEqual(sorted(self.graph.nodes()),
['a', 'b', 'c', 'd', 'e', 'f'])
self.assertListEqual(hf.recursive_sorted(self.graph.edges()),
hf.recursive_sorted([('a', 'b'), ('b', 'c'),
('d', 'e'), ('e', 'f')]))
def test_add_edges_from_nonstring(self):
self.graph.add_edges_from([(1, 2), (2, 3)])
def test_number_of_neighbors(self):
self.graph.add_edges_from([('a', 'b'), ('b', 'c')])
self.assertEqual(len(self.graph.neighbors('b')), 2)
def tearDown(self):
del self.graph
class TestUndirectedGraphCreation(unittest.TestCase):
def setUp(self):
self.graph = UndirectedGraph()
def test_class_init_without_data(self):
self.assertIsInstance(self.graph, UndirectedGraph)
def test_class_init_with_data_string(self):
self.G = UndirectedGraph([('a', 'b'), ('b', 'c')])
self.assertListEqual(sorted(self.G.nodes()), ['a', 'b', 'c'])
self.assertListEqual(hf.recursive_sorted(self.G.edges()),
[['a', 'b'], ['b', 'c']])
def test_add_node_string(self):
self.graph.add_node('a')
self.assertListEqual(self.graph.nodes(), ['a'])
def test_add_node_nonstring(self):
self.graph.add_node(1)
self.assertListEqual(self.graph.nodes(), [1])
def test_add_nodes_from_string(self):
self.graph.add_nodes_from(['a', 'b', 'c', 'd'])
self.assertListEqual(sorted(self.graph.nodes()),
['a', 'b', 'c', 'd'])
def test_add_nodes_from_non_string(self):
self.graph.add_nodes_from([1, 2, 3, 4])
def test_add_edge_string(self):
self.graph.add_edge('d', 'e')
self.assertListEqual(sorted(self.graph.nodes()), ['d', 'e'])
self.assertListEqual(hf.recursive_sorted(self.graph.edges()),
[['d', 'e']])
self.graph.add_nodes_from(['a', 'b', 'c'])
self.graph.add_edge('a', 'b')
self.assertListEqual(hf.recursive_sorted(self.graph.edges()),
[['a', 'b'], ['d', 'e']])
def test_add_edge_nonstring(self):
self.graph.add_edge(1, 2)
def test_add_edges_from_string(self):
self.graph.add_edges_from([('a', 'b'), ('b', 'c')])
self.assertListEqual(sorted(self.graph.nodes()), ['a', 'b', 'c'])
self.assertListEqual(hf.recursive_sorted(self.graph.edges()),
[['a', 'b'], ['b', 'c']])
self.graph.add_nodes_from(['d', 'e', 'f'])
self.graph.add_edges_from([('d', 'e'), ('e', 'f')])
self.assertListEqual(sorted(self.graph.nodes()),
['a', 'b', 'c', 'd', 'e', 'f'])
self.assertListEqual(hf.recursive_sorted(self.graph.edges()),
hf.recursive_sorted([('a', 'b'), ('b', 'c'),
('d', 'e'), ('e', 'f')]))
def test_add_edges_from_nonstring(self):
self.graph.add_edges_from([(1, 2), (2, 3)])
def test_number_of_neighbors(self):
self.graph.add_edges_from([('a', 'b'), ('b', 'c')])
self.assertEqual(len(self.graph.neighbors('b')), 2)
def tearDown(self):
del self.graph
def build_skeleton(nodes, independencies):
"""Estimates a graph skeleton (UndirectedGraph) from a set of independencies
using (the first part of) the PC algorithm. The independencies can either be
provided as an instance of the `Independencies`-class or by passing a
decision function that decides any conditional independency assertion.
Returns a tuple `(skeleton, separating_sets)`.
If an Independencies-instance is passed, the contained IndependenceAssertions
have to admit a faithful BN representation. This is the case if
they are obtained as a set of d-seperations of some Bayesian network or
if the independence assertions are closed under the semi-graphoid axioms.
Otherwise the procedure may fail to identify the correct structure.
Parameters
----------
nodes: list, array-like
A list of node/variable names of the network skeleton.
independencies: Independencies-instance or function.
The source of independency information from which to build the skeleton.
The provided Independencies should admit a faithful representation.
Can either be provided as an Independencies()-instance or by passing a
function `f(X, Y, Zs)` that returns `True` when X _|_ Y | Zs,
otherwise `False`. (X, Y being individual nodes and Zs a list of nodes).
Returns
-------
skeleton: UndirectedGraph
An estimate for the undirected graph skeleton of the BN underlying the data.
separating_sets: dict
A dict containing for each pair of not directly connected nodes a
separating set ("witnessing set") of variables that makes then
conditionally independent. (needed for edge orientation procedures)
Reference
---------
[1] Neapolitan, Learning Bayesian Networks, Section 10.1.2, Algorithm 10.2 (page 550)
http://www.cs.technion.ac.il/~dang/books/Learning%20Bayesian%20Networks(Neapolitan,%20Richard).pdf
[2] Koller & Friedman, Probabilistic Graphical Models - Principles and Techniques, 2009
Section 3.4.2.1 (page 85), Algorithm 3.3
Examples
--------
>>> from pgmpy.estimators import ConstraintBasedEstimator
>>> from pgmpy.models import BayesianModel
>>> from pgmpy.independencies import Independencies
>>> # build skeleton from list of independencies:
... ind = Independencies(['B', 'C'], ['A', ['B', 'C'], 'D'])
>>> # we need to compute closure, otherwise this set of independencies doesn't
... # admit a faithful representation:
... ind = ind.closure()
>>> skel, sep_sets = ConstraintBasedEstimator.build_skeleton("ABCD", ind)
>>> print(skel.edges())
[('A', 'D'), ('B', 'D'), ('C', 'D')]
>>> # build skeleton from d-seperations of BayesianModel:
... model = BayesianModel([('A', 'C'), ('B', 'C'), ('B', 'D'), ('C', 'E')])
>>> skel, sep_sets = ConstraintBasedEstimator.build_skeleton(model.nodes(), model.get_independencies())
>>> print(skel.edges())
[('A', 'C'), ('B', 'C'), ('B', 'D'), ('C', 'E')]
"""
nodes = list(nodes)
if isinstance(independencies, Independencies):
def is_independent(X, Y, Zs):
return IndependenceAssertion(X, Y, Zs) in independencies
elif callable(independencies):
is_independent = independencies
else:
raise ValueError(
"'independencies' must be either Independencies-instance " +
"or a ternary function that decides independencies.")
graph = UndirectedGraph(combinations(nodes, 2))
lim_neighbors = 0
separating_sets = dict()
while not all(
[len(graph.neighbors(node)) < lim_neighbors for node in nodes]):
for node in nodes:
for neighbor in graph.neighbors(node):
# search if there is a set of neighbors (of size lim_neighbors)
# that makes X and Y independent:
for separating_set in combinations(
set(graph.neighbors(node)) - set([neighbor]),
lim_neighbors):
if is_independent(node, neighbor, separating_set):
separating_sets[frozenset(
(node, neighbor))] = separating_set
graph.remove_edge(node, neighbor)
break
lim_neighbors += 1
return graph, separating_sets
class TestUndirectedGraphCreation(unittest.TestCase):
def setUp(self):
self.graph = UndirectedGraph()
def test_class_init_without_data(self):
self.assertIsInstance(self.graph, UndirectedGraph)
def test_class_init_with_data_string(self):
self.G = UndirectedGraph([("a", "b"), ("b", "c")])
self.assertListEqual(sorted(self.G.nodes()), ["a", "b", "c"])
self.assertListEqual(hf.recursive_sorted(self.G.edges()),
[["a", "b"], ["b", "c"]])
def test_add_node_string(self):
self.graph.add_node("a")
self.assertListEqual(list(self.graph.nodes()), ["a"])
def test_add_node_nonstring(self):
self.graph.add_node(1)
self.assertListEqual(list(self.graph.nodes()), [1])
def test_add_nodes_from_string(self):
self.graph.add_nodes_from(["a", "b", "c", "d"])
self.assertListEqual(sorted(self.graph.nodes()), ["a", "b", "c", "d"])
def test_add_node_with_weight(self):
self.graph.add_node("a")
self.graph.add_node("weight_a", weight=0.3)
self.assertEqual(self.graph.nodes["weight_a"]["weight"], 0.3)
self.assertEqual(self.graph.nodes["a"]["weight"], None)
def test_add_nodes_from_with_weight(self):
self.graph.add_node(1)
self.graph.add_nodes_from(["weight_b", "weight_c"], weights=[0.3, 0.5])
self.assertEqual(self.graph.nodes["weight_b"]["weight"], 0.3)
self.assertEqual(self.graph.nodes["weight_c"]["weight"], 0.5)
self.assertEqual(self.graph.nodes[1]["weight"], None)
def test_add_nodes_from_non_string(self):
self.graph.add_nodes_from([1, 2, 3, 4])
def test_add_edge_string(self):
self.graph.add_edge("d", "e")
self.assertListEqual(sorted(self.graph.nodes()), ["d", "e"])
self.assertListEqual(hf.recursive_sorted(self.graph.edges()),
[["d", "e"]])
self.graph.add_nodes_from(["a", "b", "c"])
self.graph.add_edge("a", "b")
self.assertListEqual(hf.recursive_sorted(self.graph.edges()),
[["a", "b"], ["d", "e"]])
def test_add_edge_nonstring(self):
self.graph.add_edge(1, 2)
def test_add_edges_from_string(self):
self.graph.add_edges_from([("a", "b"), ("b", "c")])
self.assertListEqual(sorted(self.graph.nodes()), ["a", "b", "c"])
self.assertListEqual(hf.recursive_sorted(self.graph.edges()),
[["a", "b"], ["b", "c"]])
self.graph.add_nodes_from(["d", "e", "f"])
self.graph.add_edges_from([("d", "e"), ("e", "f")])
self.assertListEqual(sorted(self.graph.nodes()),
["a", "b", "c", "d", "e", "f"])
self.assertListEqual(
hf.recursive_sorted(self.graph.edges()),
hf.recursive_sorted([("a", "b"), ("b", "c"), ("d", "e"),
("e", "f")]),
)
def test_add_edges_from_nonstring(self):
self.graph.add_edges_from([(1, 2), (2, 3)])
def test_number_of_neighbors(self):
self.graph.add_edges_from([("a", "b"), ("b", "c")])
self.assertEqual(len(list(self.graph.neighbors("b"))), 2)
def tearDown(self):
del self.graph
def build_skeleton(nodes, independencies):
"""Estimates a graph skeleton (UndirectedGraph) from a set of independencies
using (the first part of) the PC algorithm. The independencies can either be
provided as an instance of the `Independencies`-class or by passing a
decision function that decides any conditional independency assertion.
Returns a tuple `(skeleton, separating_sets)`.
If an Independencies-instance is passed, the contained IndependenceAssertions
have to admit a faithful BN representation. This is the case if
they are obtained as a set of d-seperations of some Bayesian network or
if the independence assertions are closed under the semi-graphoid axioms.
Otherwise the procedure may fail to identify the correct structure.
Parameters
----------
nodes: list, array-like
A list of node/variable names of the network skeleton.
independencies: Independencies-instance or function.
The source of independency information from which to build the skeleton.
The provided Independencies should admit a faithful representation.
Can either be provided as an Independencies()-instance or by passing a
function `f(X, Y, Zs)` that returns `True` when X _|_ Y | Zs,
otherwise `False`. (X, Y being individual nodes and Zs a list of nodes).
Returns
-------
skeleton: UndirectedGraph
An estimate for the undirected graph skeleton of the BN underlying the data.
separating_sets: dict
A dict containing for each pair of not directly connected nodes a
separating set ("witnessing set") of variables that makes then
conditionally independent. (needed for edge orientation procedures)
Reference
---------
[1] Neapolitan, Learning Bayesian Networks, Section 10.1.2, Algorithm 10.2 (page 550)
http://www.cs.technion.ac.il/~dang/books/Learning%20Bayesian%20Networks(Neapolitan,%20Richard).pdf
[2] Koller & Friedman, Probabilistic Graphical Models - Principles and Techniques, 2009
Section 3.4.2.1 (page 85), Algorithm 3.3
Examples
--------
>>> from pgmpy.estimators import ConstraintBasedEstimator
>>> from pgmpy.models import BayesianModel
>>> from pgmpy.independencies import Independencies
>>> # build skeleton from list of independencies:
... ind = Independencies(['B', 'C'], ['A', ['B', 'C'], 'D'])
>>> # we need to compute closure, otherwise this set of independencies doesn't
... # admit a faithful representation:
... ind = ind.closure()
>>> skel, sep_sets = ConstraintBasedEstimator.build_skeleton("ABCD", ind)
>>> print(skel.edges())
[('A', 'D'), ('B', 'D'), ('C', 'D')]
>>> # build skeleton from d-seperations of BayesianModel:
... model = BayesianModel([('A', 'C'), ('B', 'C'), ('B', 'D'), ('C', 'E')])
>>> skel, sep_sets = ConstraintBasedEstimator.build_skeleton(model.nodes(), model.get_independencies())
>>> print(skel.edges())
[('A', 'C'), ('B', 'C'), ('B', 'D'), ('C', 'E')]
"""
nodes = list(nodes)
if isinstance(independencies, Independencies):
def is_independent(X, Y, Zs):
return IndependenceAssertion(X, Y, Zs) in independencies
elif callable(independencies):
is_independent = independencies
else:
raise ValueError("'independencies' must be either Independencies-instance " +
"or a ternary function that decides independencies.")
graph = UndirectedGraph(combinations(nodes, 2))
lim_neighbors = 0
separating_sets = dict()
while not all([len(graph.neighbors(node)) < lim_neighbors for node in nodes]):
for node in nodes:
for neighbor in graph.neighbors(node):
# search if there is a set of neighbors (of size lim_neighbors)
# that makes X and Y independent:
for separating_set in combinations(set(graph.neighbors(node)) - set([neighbor]), lim_neighbors):
if is_independent(node, neighbor, separating_set):
separating_sets[frozenset((node, neighbor))] = separating_set
graph.remove_edge(node, neighbor)
break
lim_neighbors += 1
return graph, separating_sets
