Fix typo in the _categorical_exact function (#1060)

This typo would cause the function to error if there was only a single shortest path.

pomegranate/bayesian_network.py

@@ -955,7 +955,7 @@ def _categorical_exact(X, sample_weight=None, include_parents=None,
 					structure=structure)
 
 	path = sorted(nx.all_shortest_paths(order_graph, source=(),
-		target=tuple(range(d)), weight="weight"))[1]
+		target=tuple(range(d)), weight="weight"))[0]
 
 	score, structure = 0, list( None for i in range(d) )
 	for u, v in zip(path[:-1], path[1:]):

tests/test_bayesian_network.py

@@ -1030,33 +1030,33 @@ def test_learn_structure_exact(X):
 	model = BayesianNetwork(algorithm='exact')
 	model.fit(X)
 
-	assert_tuple_equal(model._parents, ((), (0, 2), (), ()))
+	assert_tuple_equal(model._parents, ((), (), (0, 1), ()))
 
 	assert_array_almost_equal(model.distributions[0].probs,
 		[[0.4545, 0.5455]], 4)
-	assert_array_almost_equal(model.distributions[3].probs, 
+	assert_array_almost_equal(model.distributions[1].probs, 
 		[[0.4545, 0.5455]], 4)
-	assert_array_almost_equal(model.distributions[2].probs,
-		[[0.5455, 0.4545]], 4)
-	assert_array_almost_equal(model.distributions[1].probs[0], 
+	assert_array_almost_equal(model.distributions[3].probs,
+		[[0.4545, 0.5455]], 4)
+	assert_array_almost_equal(model.distributions[2].probs[0], 
 		[[[0.3333, 0.6667],
           [1.0000, 0.0000]],
 
-         [[0.3333, 0.6667],
-          [0.3333, 0.6667]]], 4)
+         [[0.5, 0.5],
+          [0.5, 0.5]]], 4)
 
 	assert_array_almost_equal(model._factor_graph.factors[0].probs, 
 		[[0.4545, 0.5455]], 4)
+	assert_array_almost_equal(model._factor_graph.factors[1].probs, 
+		[[0.4545, 0.5455]], 4)
 	assert_array_almost_equal(model._factor_graph.factors[3].probs, 
 		[[0.4545, 0.5455]], 4)
 	assert_array_almost_equal(model._factor_graph.factors[2].probs, 
-		[[0.5455, 0.4545]], 4)
-	assert_array_almost_equal(model._factor_graph.factors[1].probs, 
 		[[[0.0833, 0.1667],
           [0.2500, 0.0000]],
 
-         [[0.0833, 0.1667],
-          [0.0833, 0.1667]]], 4)
+         [[0.1250, 0.1250],
+          [0.1250, 0.1250]]], 4)
 
 
 def test_summarize(X, distributions):

tests/test_bayesian_network_structure_learning.py

@@ -152,15 +152,15 @@ def test_categorical_chow_liu_raises(X, w):
 
 def test_categorical_exact(X):
 	structure = _categorical_exact(X)
-	assert_tuple_equal(structure, ((), (0,), (), (0, 1)))
+	assert_tuple_equal(structure, ((), (0,), (0, 1), ()))
 
 	structure = _categorical_exact(X, max_parents=1)
 	assert_tuple_equal(structure, ((), (0,), (), ()))
 
 
 def test_categorical_exact_weighted(X, w):
 	structure = _categorical_exact(X, w)
-	assert_tuple_equal(structure, ((), (0,), (), (0, 1)))
+	assert_tuple_equal(structure, ((), (0,), (0, 1), ()))
 
 	structure = _categorical_exact(X, w, max_parents=1)
 	assert_tuple_equal(structure, ((), (0,), (), ()))
@@ -169,15 +169,15 @@ def test_categorical_exact_weighted(X, w):
 def test_categorical_exact_exclude_parents(X):
 	exclude_parents = ((), (2,), (), (1,))
 	structure = _categorical_exact(X, exclude_parents=exclude_parents)
-	assert_tuple_equal(structure, ((), (), (0, 3), (0,)))
+	assert_tuple_equal(structure, ((), (), (0,), (0, 2)))
 
 	structure = _categorical_exact(X, exclude_parents=exclude_parents, 
 		max_parents=1)
-	assert_tuple_equal(structure, ((), (), (0,), ()))
+	assert_tuple_equal(structure, ((), (0,), (), ()))
 
 	exclude_parents = ((), (2,), (), (0, 1))
 	structure = _categorical_exact(X, exclude_parents=exclude_parents)
-	assert_tuple_equal(structure, ((3,), (), (0,3), ()))
+	assert_tuple_equal(structure, ((2, 3), (), (), (2,)))
 
 
 def test_categorical_exact_large():