def test_find_MAP():
print '-' * 80
G = MarkovModel()
G.add_nodes_from(['x1', 'x2', 'x3'])
G.add_edges_from([('x1', 'x2'), ('x1', 'x3')])
phi = [
DiscreteFactor(['x2', 'x1'],
cardinality=[2, 2],
values=np.array([[1.0 / 1, 1.0 / 2], [1.0 / 3,
1.0 / 4]])),
DiscreteFactor(['x3', 'x1'],
cardinality=[2, 2],
values=np.array([[1.0 / 1, 1.0 / 2], [1.0 / 3,
1.0 / 4]]))
]
# DiscreteFactor(['x1'], cardinality=[2],
# values=np.array([2,2]))]
G.add_factors(*phi)
print "nodes:", G.nodes()
bp = BeliefPropagation(G)
bp.max_calibrate()
# bp.calibrate()
clique_beliefs = bp.get_clique_beliefs()
print clique_beliefs
print clique_beliefs[('x1', 'x2')]
print clique_beliefs[('x1', 'x3')]
# print 'partition function should be', np.sum(clique_beliefs[('x1', 'x3')].values)
phi_query = bp._query(['x1', 'x2', 'x3'], operation='maximize')
# phi_query = bp._query(['x1', 'x2', 'x3'], operation='marginalize')
print phi_query
sleep(52)
def get_partition_function_BP(G):
'''
Calculate partition function of G using belief propogation
'''
bp = BeliefPropagation(G)
bp.calibrate()
clique_beliefs = bp.get_clique_beliefs()
partition_function = np.sum(clique_beliefs.values()[0].values)
return partition_function
def find_MAP_val(G):
'''
Inputs:
- G: MarkovModel
'''
bp = BeliefPropagation(G)
bp.max_calibrate()
clique_beliefs = bp.get_clique_beliefs()
map_val = np.max(clique_beliefs.values()[0].values)
return map_val
def find_MAP_state(G):
'''
Inputs:
- G: MarkovModel
'''
bp = BeliefPropagation(G)
bp.max_calibrate()
clique_beliefs = bp.get_clique_beliefs()
phi_query = bp._query(G.nodes(), operation='maximize')
print phi_query
return phi_query
class IsingModel:
def __init__(self, theta, seed=None):
if seed is not None:
np.random.seed(seed)
# graph
self.G = MarkovModel()
for _, row in theta.iterrows():
# unary
if row["j"]==row["k"]:
self.G.add_node(str(int(row["j"])))
theta_jj = row["value"]
self.G.add_factors(DiscreteFactor([str(int(row["j"]))], [2],
np.exp([-theta_jj,theta_jj])))
# pairwise
elif row["value"]!=0:
self.G.add_edge(str(int(row["j"])), str(int(row["k"])))
theta_jk = row["value"]
self.G.add_factors(DiscreteFactor([str(int(row["j"])), str(int(row["k"]))],
[2, 2], np.exp([theta_jk, -theta_jk, -theta_jk, theta_jk])))
self.G.check_model()
self.infer = BeliefPropagation(self.G)
self.infer.calibrate()
def get_moments(self):
p = len(list(self.G.nodes))
factor_dict = self.infer.get_clique_beliefs()
mom_matrix = np.zeros([p,p])
for clique in factor_dict:
for pair in it.combinations(clique,2):
moment = factor_dict[clique].marginalize(set(clique).difference(set(pair)),inplace=False)
moment = moment.normalize(inplace=False)
pair_int = [int(x) for x in pair]
moment = moment.values[0,0]+moment.values[1,1]-moment.values[0,1]-moment.values[1,0]
mom_matrix[pair_int[0],pair_int[1]] = moment
mom_matrix[pair_int[1],pair_int[0]] = moment
for unary in it.combinations(clique,1):
unary_int = [int(x) for x in unary][0]
moment = factor_dict[clique].marginalize(set(clique).difference(set(unary)),inplace=False).normalize(inplace=False).values
moment = moment[1]-moment[0]
mom_matrix[unary_int,unary_int] = moment
return mom_matrix
def test_max_calibrate_clique_belief(self):
belief_propagation = BeliefPropagation(self.junction_tree)
belief_propagation.max_calibrate()
clique_belief = belief_propagation.get_clique_beliefs()
phi1 = Factor(['A', 'B'], [2, 3], range(6))
phi2 = Factor(['B', 'C'], [3, 2], range(6))
phi3 = Factor(['C', 'D'], [2, 2], range(4))
b_A_B = phi1 * (phi3.maximize(['D'], inplace=False) * phi2).maximize(['C'], inplace=False)
b_B_C = phi2 * (phi1.maximize(['A'], inplace=False) * phi3.maximize(['D'], inplace=False))
b_C_D = phi3 * (phi1.maximize(['A'], inplace=False) * phi2).maximize(['B'], inplace=False)
np_test.assert_array_almost_equal(clique_belief[('A', 'B')].values, b_A_B.values)
np_test.assert_array_almost_equal(clique_belief[('B', 'C')].values, b_B_C.values)
np_test.assert_array_almost_equal(clique_belief[('C', 'D')].values, b_C_D.values)
def test_max_calibrate_clique_belief(self):
belief_propagation = BeliefPropagation(self.junction_tree)
belief_propagation.max_calibrate()
clique_belief = belief_propagation.get_clique_beliefs()
phi1 = Factor(['A', 'B'], [2, 3], range(6))
phi2 = Factor(['B', 'C'], [3, 2], range(6))
phi3 = Factor(['C', 'D'], [2, 2], range(4))
b_A_B = phi1 * (phi3.maximize(['D'], inplace=False) * phi2).maximize(
['C'], inplace=False)
b_B_C = phi2 * (phi1.maximize(['A'], inplace=False) *
phi3.maximize(['D'], inplace=False))
b_C_D = phi3 * (phi1.maximize(['A'], inplace=False) * phi2).maximize(
['B'], inplace=False)
np_test.assert_array_almost_equal(clique_belief[('A', 'B')].values,
b_A_B.values)
np_test.assert_array_almost_equal(clique_belief[('B', 'C')].values,
b_B_C.values)
np_test.assert_array_almost_equal(clique_belief[('C', 'D')].values,
b_C_D.values)
def test_max_calibrate_clique_belief(self):
belief_propagation = BeliefPropagation(self.junction_tree)
belief_propagation.max_calibrate()
clique_belief = belief_propagation.get_clique_beliefs()
phi1 = DiscreteFactor(["A", "B"], [2, 3], range(6))
phi2 = DiscreteFactor(["B", "C"], [3, 2], range(6))
phi3 = DiscreteFactor(["C", "D"], [2, 2], range(4))
b_A_B = phi1 * (phi3.maximize(["D"], inplace=False) * phi2).maximize(
["C"], inplace=False)
b_B_C = phi2 * (phi1.maximize(["A"], inplace=False) *
phi3.maximize(["D"], inplace=False))
b_C_D = phi3 * (phi1.maximize(["A"], inplace=False) * phi2).maximize(
["B"], inplace=False)
np_test.assert_array_almost_equal(clique_belief[("A", "B")].values,
b_A_B.values)
np_test.assert_array_almost_equal(clique_belief[("B", "C")].values,
b_B_C.values)
np_test.assert_array_almost_equal(clique_belief[("C", "D")].values,
b_C_D.values)
('traffic_jam', 'long_queues'),
('traffic_jam', 'late_for_school'),
('getting_up_late', 'late_for_school')])
cpd_rain = TabularCPD('rain', 2, [[0.4], [0.6]])
cpd_accident = TabularCPD('accident', 2, [[0.2], [0.8]])
cpd_traffic_jam = TabularCPD('traffic_jam', 2,
[[0.9, 0.6, 0.7, 0.1],
[0.1, 0.4, 0.3, 0.9]],
evidence=['rain',
'accident'],
evidence_card=[2, 2])
cpd_getting_up_late = TabularCPD('getting_up_late', 2, [[0.6], [0.4]])
cpd_late_for_school = TabularCPD('late_for_school', 2,
[[0.9, 0.45, 0.8, 0.1],
[0.1, 0.55, 0.2, 0.9]],
evidence=['getting_up_late','traffic_jam'],
evidence_card=[2, 2])
cpd_long_queues = TabularCPD('long_queues', 2,
[[0.9, 0.2],
[0.1, 0.8]],
evidence=['traffic_jam'],
evidence_card=[2])
model.add_cpds(cpd_rain, cpd_accident,
cpd_traffic_jam, cpd_getting_up_late,
cpd_late_for_school, cpd_long_queues)
belief_propagation = BeliefPropagation(model)
# To calibrate the clique tree, use calibrate() method
belief_propagation.calibrate()
# To get cluster (or clique) beliefs use the corresponding getters
belief_propagation.get_clique_beliefs()