def random_dag(number_of_nodes: int = 5,
edge_density: float = 0.4,
max_in_degree: int = 4) -> DAG:
"""Create a connected, random directed acyclic graph (DAG), with the given number of nodes,
the given edge density, and with no node exceeding having too high in degree"""
node_names = [f"X{i}" for i in range(number_of_nodes)]
dag = DAG()
# First make sure the dag is connected
visited = list()
unvisited = list(node_names)
node = random.choice(unvisited)
unvisited.remove(node)
visited.append(node)
dag.add_node(node)
while unvisited:
node = random.choice(unvisited)
neighbor = random.choice(visited)
if node_names.index(node) < node_names.index(
neighbor) and dag.in_degree(neighbor) < max_in_degree:
dag.add_edge(node, neighbor)
elif node_names.index(neighbor) < node_names.index(node):
dag.add_edge(neighbor, node)
else:
continue
unvisited.remove(node)
visited.append(node)
# Then add edges until desired density is reached
maximum_number_of_edges = number_of_nodes * (number_of_nodes - 1) / 2
while dag.number_of_edges() < int(edge_density * maximum_number_of_edges):
add_random_edge(dag, node_names)
return dag
def add_random_edge(dag: DAG,
node_order: List[str],
max_in_degree: int = 4) -> None:
"""Add a random edge to the graph, that respects the given node_order, and
also doesn't add a link if the sampled node has maximal in_degree already.
It may not add any edge.
"""
n1, n2 = random.sample(node_order, 2)
if node_order.index(n1) < node_order.index(n2) and dag.in_degree(
n2) < max_in_degree:
dag.add_edge(n1, n2)
elif node_order.index(n2) < node_order.index(n1) and dag.in_degree(
n1) < max_in_degree:
dag.add_edge(n2, n1)
class TestDAGCreation(unittest.TestCase):
def setUp(self):
self.graph = DAG()
def test_class_init_without_data(self):
self.assertIsInstance(self.graph, DAG)
def test_class_init_with_data_string(self):
self.graph = DAG([("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"]]
)
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)
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_node_weight(self):
self.graph.add_node("weighted_a", 0.3)
self.assertEqual(self.graph.nodes["weighted_a"]["weight"], 0.3)
def test_add_nodes_from_weight(self):
self.graph.add_nodes_from(["weighted_b", "weighted_c"], [0.5, 0.6])
self.assertEqual(self.graph.nodes["weighted_b"]["weight"], 0.5)
self.assertEqual(self.graph.nodes["weighted_c"]["weight"], 0.6)
self.graph.add_nodes_from(["e", "f"])
self.assertEqual(self.graph.nodes["e"]["weight"], None)
self.assertEqual(self.graph.nodes["f"]["weight"], None)
def test_add_edge_string(self):
self.graph.add_edge("d", "e")
self.assertListEqual(sorted(self.graph.nodes()), ["d", "e"])
self.assertListEqual(list(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_add_edge_weight(self):
self.graph.add_edge("a", "b", weight=0.3)
if nx.__version__.startswith("1"):
self.assertEqual(self.graph.edge["a"]["b"]["weight"], 0.3)
else:
self.assertEqual(self.graph.adj["a"]["b"]["weight"], 0.3)
def test_add_edges_from_weight(self):
self.graph.add_edges_from([("b", "c"), ("c", "d")], weights=[0.5, 0.6])
if nx.__version__.startswith("1"):
self.assertEqual(self.graph.edge["b"]["c"]["weight"], 0.5)
self.assertEqual(self.graph.edge["c"]["d"]["weight"], 0.6)
self.graph.add_edges_from([("e", "f")])
self.assertEqual(self.graph.edge["e"]["f"]["weight"], None)
else:
self.assertEqual(self.graph.adj["b"]["c"]["weight"], 0.5)
self.assertEqual(self.graph.adj["c"]["d"]["weight"], 0.6)
self.graph.add_edges_from([("e", "f")])
self.assertEqual(self.graph.adj["e"]["f"]["weight"], None)
def test_update_node_parents_bm_constructor(self):
self.graph = DAG([("a", "b"), ("b", "c")])
self.assertListEqual(list(self.graph.predecessors("a")), [])
self.assertListEqual(list(self.graph.predecessors("b")), ["a"])
self.assertListEqual(list(self.graph.predecessors("c")), ["b"])
def test_update_node_parents(self):
self.graph.add_nodes_from(["a", "b", "c"])
self.graph.add_edges_from([("a", "b"), ("b", "c")])
self.assertListEqual(list(self.graph.predecessors("a")), [])
self.assertListEqual(list(self.graph.predecessors("b")), ["a"])
self.assertListEqual(list(self.graph.predecessors("c")), ["b"])
def test_get_leaves(self):
self.graph.add_edges_from(
[("A", "B"), ("B", "C"), ("B", "D"), ("D", "E"), ("D", "F"), ("A", "G")]
)
self.assertEqual(sorted(self.graph.get_leaves()), sorted(["C", "G", "E", "F"]))
def test_get_roots(self):
self.graph.add_edges_from(
[("A", "B"), ("B", "C"), ("B", "D"), ("D", "E"), ("D", "F"), ("A", "G")]
)
self.assertEqual(["A"], self.graph.get_roots())
self.graph.add_edge("H", "G")
self.assertEqual(sorted(["A", "H"]), sorted(self.graph.get_roots()))
def test_init_with_cycle(self):
self.assertRaises(ValueError, DAG, [("a", "a")])
self.assertRaises(ValueError, DAG, [("a", "b"), ("b", "a")])
self.assertRaises(ValueError, DAG, [("a", "b"), ("b", "c"), ("c", "a")])
def tearDown(self):
del self.graph
def pdag_to_dag(pdag):
"""Completes a PDAG to a DAG, without adding v-structures, if such a
completion exists. If no faithful extension is possible, some fully
oriented DAG that corresponds to the PDAG is returned and a warning is
generated. This is a static method.
Parameters
----------
pdag: DAG
A directed acyclic graph pattern, consisting in (acyclic) directed edges
as well as "undirected" edges, represented as both-way edges between
nodes.
Returns
-------
dag: DAG
A faithful orientation of pdag, if one exists. Otherwise any
fully orientated DAG/BayesianModel with the structure of pdag.
References
----------
[1] Chickering, Learning Equivalence Classes of Bayesian-Network Structures,
2002; See page 454 (last paragraph) for the algorithm pdag_to_dag
http://www.jmlr.org/papers/volume2/chickering02a/chickering02a.pdf
[2] Dor & Tarsi, A simple algorithm to construct a consistent extension
of a partially oriented graph, 1992,
http://ftp.cs.ucla.edu/pub/stat_ser/r185-dor-tarsi.pdf
Examples
--------
>>> import pandas as pd
>>> import numpy as np
>>> from pgmpy.base import DAG
>>> from pgmpy.estimators import ConstraintBasedEstimator
>>> data = pd.DataFrame(np.random.randint(0, 4, size=(5000, 3)), columns=list('ABD'))
>>> data['C'] = data['A'] - data['B']
>>> data['D'] += data['A']
>>> c = ConstraintBasedEstimator(data)
>>> pdag = c.skeleton_to_pdag(*c.estimate_skeleton())
>>> pdag.edges()
[('B', 'C'), ('D', 'A'), ('A', 'D'), ('A', 'C')]
>>> c.pdag_to_dag(pdag).edges()
[('B', 'C'), ('A', 'D'), ('A', 'C')]
>>> # pdag_to_dag is static:
... pdag1 = DAG([('A', 'B'), ('C', 'B'), ('C', 'D'), ('D', 'C'), ('D', 'A'), ('A', 'D')])
>>> ConstraintBasedEstimator.pdag_to_dag(pdag1).edges()
[('D', 'C'), ('C', 'B'), ('A', 'B'), ('A', 'D')]
>>> # example of a pdag with no faithful extension:
... pdag2 = DAG([('A', 'B'), ('A', 'C'), ('B', 'C'), ('C', 'B')])
>>> ConstraintBasedEstimator.pdag_to_dag(pdag2).edges()
UserWarning: PDAG has no faithful extension (= no oriented DAG with the same v-structures as PDAG).
Remaining undirected PDAG edges oriented arbitrarily.
[('B', 'C'), ('A', 'B'), ('A', 'C')]
"""
pdag = pdag.copy()
dag = DAG()
dag.add_nodes_from(pdag.nodes())
# add already directed edges of pdag to dag
for X, Y in pdag.edges():
if not pdag.has_edge(Y, X):
dag.add_edge(X, Y)
while pdag.number_of_nodes() > 0:
# find node with (1) no directed outgoing edges and
# (2) the set of undirected neighbors is either empty or
# undirected neighbors + parents of X are a clique
found = False
for X in pdag.nodes():
directed_outgoing_edges = set(pdag.successors(X)) - set(
pdag.predecessors(X))
undirected_neighbors = set(pdag.successors(X)) & set(
pdag.predecessors(X))
neighbors_are_clique = all((pdag.has_edge(Y, Z)
for Z in pdag.predecessors(X)
for Y in undirected_neighbors
if not Y == Z))
if not directed_outgoing_edges and (not undirected_neighbors
or neighbors_are_clique):
found = True
# add all edges of X as outgoing edges to dag
for Y in pdag.predecessors(X):
dag.add_edge(Y, X)
pdag.remove_node(X)
break
if not found:
warn(
"PDAG has no faithful extension (= no oriented DAG with the "
+
"same v-structures as PDAG). Remaining undirected PDAG edges "
+ "oriented arbitrarily.")
for X, Y in pdag.edges():
if not dag.has_edge(Y, X):
try:
dag.add_edge(X, Y)
except ValueError:
pass
break
return dag