def moralize(self):
"""
Removes all the immoralities in the Network and creates a moral
graph (UndirectedGraph).
A v-structure X->Z<-Y is an immorality if there is no directed edge
between X and Y.
Examples
--------
>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> dbn = DBN([(('D',0), ('G',0)), (('I',0), ('G',0))])
>>> moral_graph = dbn.moralize()
>>> moral_graph.edges()
[(('G', 0), ('I', 0)),
(('G', 0), ('D', 0)),
(('D', 1), ('I', 1)),
(('D', 1), ('G', 1)),
(('I', 0), ('D', 0)),
(('G', 1), ('I', 1))]
"""
moral_graph = UndirectedGraph(self.to_undirected().edges())
for node in super().nodes():
moral_graph.add_edges_from(itertools.combinations(
self.get_parents(node), 2))
return moral_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 moralize(self):
"""
Removes all the immoralities in the DirectedGraph and creates a moral
graph (UndirectedGraph).
A v-structure X->Z<-Y is an immorality if there is no directed edge
between X and Y.
Examples
--------
>>> from pgmpy.base import DirectedGraph
>>> G = DirectedGraph(ebunch=[('diff', 'grade'), ('intel', 'grade')])
>>> moral_graph = G.moralize()
>>> moral_graph.edges()
[('intel', 'grade'), ('intel', 'diff'), ('grade', 'diff')]
"""
moral_graph = UndirectedGraph(self.to_undirected().edges())
for node in self.nodes():
moral_graph.add_edges_from(
itertools.combinations(self.get_parents(node), 2))
return moral_graph
def moralize(self):
"""
Removes all the immoralities in the DirectedGraph and creates a moral
graph (UndirectedGraph).
A v-structure X->Z<-Y is an immorality if there is no directed edge
between X and Y.
Examples
--------
>>> from pgmpy.base import DirectedGraph
>>> G = DirectedGraph(ebunch=[('diff', 'grade'), ('intel', 'grade')])
>>> moral_graph = G.moralize()
>>> moral_graph.edges()
[('intel', 'grade'), ('intel', 'diff'), ('grade', 'diff')]
"""
moral_graph = UndirectedGraph(self.to_undirected().edges())
for node in self.nodes():
moral_graph.add_edges_from(
itertools.combinations(self.get_parents(node), 2))
return moral_graph
def mmpc(self, significance_level=0.01):
nodes = self.state_names.keys()
def assoc(X, Y, Zs):
"""Measure for (conditional) association between variables. Use negative
p-value of independence test.
"""
return 1 - chi_square(X, Y, Zs, self.data)[1]
def min_assoc(X, Y, Zs):
"Minimal association of X, Y given any subset of Zs."
return min(assoc(X, Y, Zs_subset) for Zs_subset in powerset(Zs))
def max_min_heuristic(X, Zs):
"Finds variable that maximizes min_assoc with `node` relative to `neighbors`."
max_min_assoc = 0
best_Y = None
for Y in set(nodes) - set(Zs + [X]):
min_assoc_val = min_assoc(X, Y, Zs)
if min_assoc_val >= max_min_assoc:
best_Y = Y
max_min_assoc = min_assoc_val
return (best_Y, max_min_assoc)
# Find parents and children for each node
neighbors = dict()
for node in nodes:
neighbors[node] = []
# Forward Phase
while True:
new_neighbor, new_neighbor_min_assoc = max_min_heuristic(
node, neighbors[node])
if new_neighbor_min_assoc > 0:
neighbors[node].append(new_neighbor)
else:
break
# Backward Phase
for neigh in neighbors[node]:
other_neighbors = [n for n in neighbors[node] if n != neigh]
for sep_set in powerset(other_neighbors):
if self.test_conditional_independence(
node, neigh, sep_set):
neighbors[node].remove(neigh)
break
# correct for false positives
for node in nodes:
print(node, ":", neighbors[node])
print(neighbors[node])
for neigh in neighbors[node]:
if node not in neighbors[neigh]:
print("node-%s is removed" % neigh)
neighbors[node].remove(neigh)
skel = UndirectedGraph()
skel.add_nodes_from(nodes)
for node in nodes:
print(node, "->", neighbors[node])
skel.add_edges_from([(node, neigh) for neigh in neighbors[node]])
return skel
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
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 mmpc(self, data, nodes):
"""
Estimates a graph skeleton (UndirectedGraph) for the data set, using the MMPC (max-min parents-and-children) algorithm.
:return: graph skeleton
"""
def is_independent(X, Y, Zs, cb_estimator):
"""
Returns result of hypothesis test for the null hypothesis that
X _|_ Y | Zs, using a chi2 statistic and threshold `significance_level`.
"""
if (tuple(sorted([X, Y])), tuple(sorted(Zs))) in self.p_val_cache:
p_value, sufficient_data = self.p_val_cache.get(
(tuple(sorted([X, Y])), tuple(sorted(Zs))))
else:
chi2, p_value, sufficient_data = cb_estimator.test_conditional_independence(
X, Y, Zs)
self.p_val_cache.update({
(tuple(sorted([X, Y])), tuple(sorted(Zs))):
(p_value, sufficient_data)
})
return p_value >= self.alpha and sufficient_data
def assoc(X, Y, Zs, cb_estimator):
"""
Measure for (conditional) association between variables. Use negative
p-value of independence test.
"""
if (tuple(sorted([X, Y])), tuple(sorted(Zs))) in self.p_val_cache:
p_value, sufficient_data = self.p_val_cache.get(
(tuple(sorted([X, Y])), tuple(sorted(Zs))))
else:
chi2, p_value, sufficient_data = cb_estimator.test_conditional_independence(
X, Y, Zs)
self.p_val_cache.update({
(tuple(sorted([X, Y])), tuple(sorted(Zs))):
(p_value, sufficient_data)
})
return 1 - p_value
def min_assoc(X, Y, Zs, cb_estimator):
"""
Minimal association of X, Y given any subset of Zs.
"""
min_association = float('inf')
for size in range(min(self.max_reach, len(Zs)) + 1):
partial_min_association = min(
assoc(X, Y, Zs_subset, cb_estimator)
for Zs_subset in combinations(Zs, size))
if partial_min_association < min_association:
min_association = partial_min_association
return min_association
def max_min_heuristic(X, Zs):
"""
Finds variable that maximizes min_assoc with `node` relative to `neighbors`.
"""
max_min_assoc = 0
best_Y = None
for Y in set(nodes) - set(Zs + [X]):
min_assoc_val = min_assoc(X, Y, Zs, cb_estimator)
if min_assoc_val >= max_min_assoc:
best_Y = Y
max_min_assoc = min_assoc_val
return best_Y, max_min_assoc
cb_estimator = BaseEstimator(data=data, complete_samples_only=False)
# Find parents and children for each node
neighbors = dict()
for node in nodes:
neighbors[node] = []
# Forward Phase
while True:
new_neighbor, new_neighbor_min_assoc = max_min_heuristic(
node, neighbors[node])
if new_neighbor_min_assoc > 0:
neighbors[node].append(new_neighbor)
else:
break
# Backward Phase
for neigh in neighbors[node]:
other_neighbors = [n for n in neighbors[node] if n != neigh]
sep_sets = [
sep_set for sep_set_size in range(
min(self.max_reach, len(other_neighbors)) + 1)
for sep_set in combinations(other_neighbors, sep_set_size)
]
for sep_set in sep_sets:
if is_independent(node, neigh, sep_set, cb_estimator):
neighbors[node].remove(neigh)
break
# correct for false positives
for node in nodes:
for neigh in neighbors[node]:
if node not in neighbors[neigh]:
neighbors[node].remove(neigh)
skel = UndirectedGraph()
skel.add_nodes_from(nodes)
for node in nodes:
skel.add_edges_from([(node, neigh) for neigh in neighbors[node]])
return skel
