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Proposed change to d-separation tests based on pytest functions and fixtures.
@pytest.fixture
def path_graph():
"""Return a path graaph of length three."""
G = nx.path_graph(3, create_using=nx.DiGraph)
G.graph["name"] = "path"
nx.freeze(G)
return G
@pytest.fixture
def fork_graph():
"""Return a three-node fork graph."""
G = nx.DiGraph(name="fork")
G.add_edges_from([(0, 1), (0, 2)])
nx.freeze(G)
return G
@pytest.fixture
def collider_graph():
"""Return a causal collider graph."""
G = nx.DiGraph(name="collider")
G.add_edges_from([(0, 2), (1, 2)])
nx.freeze(G)
return G
@pytest.fixture
def naive_bayes_graph():
"""Return a simple Naive Bayes PGM graph."""
G = nx.DiGraph(name="naive_bayes")
G.add_edges_from([(0, 1), (0, 2), (0, 3), (0, 4)])
nx.freeze(G)
return G
@pytest.fixture
def asia_graph():
"""Return the "asia" PGM graph."""
G = nx.DiGraph(name="asia")
G.add_edges_from(
[
('asia', 'tuberculosis'),
('smoking', 'cancer'),
('smoking', 'bronchitis'),
('tuberculosis', 'either'),
('cancer', 'either'),
('either', 'xray'),
('either', 'dyspnea'),
('bronchitis', 'dyspnea')
]
)
nx.freeze(G)
return G
@pytest.mark.parametrize(
"graph", [
path_graph(),
fork_graph(),
collider_graph(),
naive_bayes_graph(),
asia_graph(),
]
)
def test_markov_condition(graph):
"""Test that the Markov condition holds for each PGM graph."""
for node in graph.nodes:
parents = set(graph.predecessors(node))
non_descendants = graph.nodes - nx.descendants(
graph, node) - {node} - parents
assert nx.d_separated(graph, {node}, non_descendants, parents)
def test_path_graph_dsep(path_graph):
"""Example-based test of d-separation for path_graph."""
assert nx.d_separated(path_graph, {0}, {2}, {1})
assert not nx.d_separated(path_graph, {0}, {2}, {})
def test_fork_graph_dsep(fork_graph):
"""Example-based test of d-separation for fork_graph."""
assert nx.d_separated(fork_graph, {1}, {2}, {0})
assert not nx.d_separated(fork_graph, {1}, {2}, {})
def test_collider_graph_dsep(collider_graph):
"""Example-based test of d-separation for collider_graph."""
assert nx.d_separated(collider_graph, {0}, {1}, {})
assert not nx.d_separated(collider_graph, {0}, {1}, {2})
def test_naive_bayes_dsep(naive_bayes_graph):
"""Example-based test of d-separation for naive_bayes_graph."""
for u, v in combinations(range(1, 5), 2):
assert nx.d_separated(naive_bayes_graph, {u}, {v}, {0})
assert not nx.d_separated(naive_bayes_graph, {u}, {v}, {})
def test_asia_graph_dsep(asia_graph):
"""Example-based test of d-separation for asia_graph."""
assert nx.d_separated(asia_graph, {'asia', 'smoking'},
{'dyspnea', 'xray'}, {'bronchitis', 'either'})
assert nx.d_separated(asia_graph, {'tuberculosis', 'cancer'},
{'bronchitis'}, {'smoking', 'xray'})
def test_undirected_graphs_are_not_supported(path_graph):
"""
Test that undirected graphs are not supported.
d-separation does not apply in the case of undirected graphs.
"""
with pytest.raises(nx.NetworkXNotImplemented):
nx.d_separated(path_graph, {0}, {1}, {2})
def test_cyclic_graphs_raise_error(self):
"""
Test that cycle graphs should cause erroring.
This is because PGMs assume a directed acyclic graph.
"""
with pytest.raises(nx.NetworkXError):
g = nx.cycle_graph(3, nx.DiGraph)
nx.d_separated(g, {0}, {1}, {2})
def test_invalid_nodes_raise_error(self):
"""
Test that graphs that have invalid nodes passed in raise errors.
"""
with pytest.raises(nx.NodeNotFound):
nx.d_separated(self.asia_G, {0}, {1}, {2})
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