def test_Asia(self):
"""Test full Asia example."""
asia = DiscreteBayesNet()
asia.add(Asia, "99/1")
asia.add(Smoking, "50/50")
asia.add(Tuberculosis, [Asia], "99/1 95/5")
asia.add(LungCancer, [Smoking], "99/1 90/10")
asia.add(Bronchitis, [Smoking], "70/30 40/60")
asia.add(Either, [Tuberculosis, LungCancer], "F T T T")
asia.add(XRay, [Either], "95/5 2/98")
asia.add(Dyspnea, [Either, Bronchitis], "9/1 2/8 3/7 1/9")
# Convert to factor graph
fg = DiscreteFactorGraph(asia)
# Create solver and eliminate
ordering = Ordering()
for j in range(8):
ordering.push_back(j)
chordal = fg.eliminateSequential(ordering)
expected2 = DiscreteDistribution(Bronchitis, "11/9")
self.gtsamAssertEquals(chordal.at(7), expected2)
# solve
actualMPE = fg.optimize()
expectedMPE = DiscreteValues()
for key in [
Asia, Dyspnea, XRay, Tuberculosis, Smoking, Either, LungCancer,
Bronchitis
]:
expectedMPE[key[0]] = 0
self.assertEqual(list(actualMPE.items()), list(expectedMPE.items()))
# Check value for MPE is the same
self.assertAlmostEqual(asia(actualMPE), fg(actualMPE))
# add evidence, we were in Asia and we have dyspnea
fg.add(Asia, "0 1")
fg.add(Dyspnea, "0 1")
# solve again, now with evidence
actualMPE2 = fg.optimize()
expectedMPE2 = DiscreteValues()
for key in [XRay, Tuberculosis, Either, LungCancer]:
expectedMPE2[key[0]] = 0
for key in [Asia, Dyspnea, Smoking, Bronchitis]:
expectedMPE2[key[0]] = 1
self.assertEqual(list(actualMPE2.items()), list(expectedMPE2.items()))
# now sample from it
chordal2 = fg.eliminateSequential(ordering)
actualSample = chordal2.sample()
self.assertEqual(len(actualSample), 8)
def test_elimination(self):
"""Test Multifrontal elimination."""
# Define DiscreteKey pairs.
keys = [(j, 2) for j in range(15)]
# Create thin-tree Bayesnet.
bayesNet = DiscreteBayesNet()
bayesNet.add(keys[0], [keys[8], keys[12]], "2/3 1/4 3/2 4/1")
bayesNet.add(keys[1], [keys[8], keys[12]], "4/1 2/3 3/2 1/4")
bayesNet.add(keys[2], [keys[9], keys[12]], "1/4 8/2 2/3 4/1")
bayesNet.add(keys[3], [keys[9], keys[12]], "1/4 2/3 3/2 4/1")
bayesNet.add(keys[4], [keys[10], keys[13]], "2/3 1/4 3/2 4/1")
bayesNet.add(keys[5], [keys[10], keys[13]], "4/1 2/3 3/2 1/4")
bayesNet.add(keys[6], [keys[11], keys[13]], "1/4 3/2 2/3 4/1")
bayesNet.add(keys[7], [keys[11], keys[13]], "1/4 2/3 3/2 4/1")
bayesNet.add(keys[8], [keys[12], keys[14]], "T 1/4 3/2 4/1")
bayesNet.add(keys[9], [keys[12], keys[14]], "4/1 2/3 F 1/4")
bayesNet.add(keys[10], [keys[13], keys[14]], "1/4 3/2 2/3 4/1")
bayesNet.add(keys[11], [keys[13], keys[14]], "1/4 2/3 3/2 4/1")
bayesNet.add(keys[12], [keys[14]], "3/1 3/1")
bayesNet.add(keys[13], [keys[14]], "1/3 3/1")
bayesNet.add(keys[14], "1/3")
# Create a factor graph out of the Bayes net.
factorGraph = DiscreteFactorGraph(bayesNet)
# Create a BayesTree out of the factor graph.
ordering = Ordering()
for j in range(15):
ordering.push_back(j)
bayesTree = factorGraph.eliminateMultifrontal(ordering)
# Uncomment these for visualization:
# print(bayesTree)
# for key in range(15):
# bayesTree[key].printSignature()
# bayesTree.saveGraph("test_DiscreteBayesTree.dot")
self.assertFalse(bayesTree.empty())
self.assertEqual(12, bayesTree.size())
# The root is P( 8 12 14), we can retrieve it by key:
root = bayesTree[8]
self.assertIsInstance(root, DiscreteBayesTreeClique)
self.assertTrue(root.isRoot())
self.assertIsInstance(root.conditional(), DiscreteConditional)
def test_constructor(self):
"""Test constructing a Bayes net."""
bayesNet = DiscreteBayesNet()
Parent, Child = (0, 2), (1, 2)
empty = DiscreteKeys()
prior = DiscreteConditional(Parent, empty, "6/4")
bayesNet.add(prior)
parents = DiscreteKeys()
parents.push_back(Parent)
conditional = DiscreteConditional(Child, parents, "7/3 8/2")
bayesNet.add(conditional)
# Check conversion to factor graph:
fg = DiscreteFactorGraph(bayesNet)
self.assertEqual(fg.size(), 2)
self.assertEqual(fg.at(1).size(), 2)
def test_sumProduct(self):
"""Test sumProduct."""
# Declare a bunch of keys
C, A, B = (0, 2), (1, 2), (2, 2)
# Create Factor graph
graph = DiscreteFactorGraph()
graph.add([C, A], "0.2 0.8 0.3 0.7")
graph.add([C, B], "0.1 0.9 0.4 0.6")
# We know MPE
mpe = DiscreteValues()
mpe[0] = 0
mpe[1] = 1
mpe[2] = 1
# Use default sumProduct
bayesNet = graph.sumProduct()
mpeProbability = bayesNet(mpe)
self.assertAlmostEqual(mpeProbability, 0.36) # regression
# Use sumProduct
for ordering_type in [
OrderingType.COLAMD, OrderingType.METIS, OrderingType.NATURAL,
OrderingType.CUSTOM
]:
bayesNet = graph.sumProduct(ordering_type)
self.assertEqual(bayesNet(mpe), mpeProbability)
def test_MPE(self):
"""Test maximum probable explanation (MPE): same as optimize."""
# Declare a bunch of keys
C, A, B = (0, 2), (1, 2), (2, 2)
# Create Factor graph
graph = DiscreteFactorGraph()
graph.add([C, A], "0.2 0.8 0.3 0.7")
graph.add([C, B], "0.1 0.9 0.4 0.6")
# We know MPE
mpe = DiscreteValues()
mpe[0] = 0
mpe[1] = 1
mpe[2] = 1
# Use maxProduct
dag = graph.maxProduct(OrderingType.COLAMD)
actualMPE = dag.argmax()
self.assertEqual(list(actualMPE.items()), list(mpe.items()))
# All in one
actualMPE2 = graph.optimize()
self.assertEqual(list(actualMPE2.items()), list(mpe.items()))
def test_optimize(self):
"""Test constructing and optizing a discrete factor graph."""
# Three keys
C = (0, 2)
B = (1, 2)
A = (2, 2)
# A simple factor graph (A)-fAC-(C)-fBC-(B)
# with smoothness priors
graph = DiscreteFactorGraph()
graph.add([A, C], "3 1 1 3")
graph.add([C, B], "3 1 1 3")
# Test optimization
expectedValues = DiscreteValues()
expectedValues[0] = 0
expectedValues[1] = 0
expectedValues[2] = 0
actualValues = graph.optimize()
self.assertEqual(list(actualValues.items()),
list(expectedValues.items()))
def test_evaluation(self):
"""Test constructing and evaluating a discrete factor graph."""
# Three keys
P1 = (0, 2)
P2 = (1, 2)
P3 = (2, 3)
# Create the DiscreteFactorGraph
graph = DiscreteFactorGraph()
# Add two unary factors (priors)
graph.add(P1, [0.9, 0.3])
graph.add(P2, "0.9 0.6")
# Add a binary factor
graph.add([P1, P2], "4 1 10 4")
# Instantiate Values
assignment = DiscreteValues()
assignment[0] = 1
assignment[1] = 1
# Check if graph evaluation works ( 0.3*0.6*4 )
self.assertAlmostEqual(.72, graph(assignment))
# Create a new test with third node and adding unary and ternary factor
graph.add(P3, "0.9 0.2 0.5")
keys = DiscreteKeys()
keys.push_back(P1)
keys.push_back(P2)
keys.push_back(P3)
graph.add(keys, "1 2 3 4 5 6 7 8 9 10 11 12")
# Below assignment selects the 8th index in the ternary factor table
assignment[0] = 1
assignment[1] = 0
assignment[2] = 1
# Check if graph evaluation works (0.3*0.9*1*0.2*8)
self.assertAlmostEqual(4.32, graph(assignment))
# Below assignment selects the 3rd index in the ternary factor table
assignment[0] = 0
assignment[1] = 1
assignment[2] = 0
# Check if graph evaluation works (0.9*0.6*1*0.9*4)
self.assertAlmostEqual(1.944, graph(assignment))
# Check if graph product works
product = graph.product()
self.assertAlmostEqual(1.944, product(assignment))