def test_query_multiple_variable(self): belief_propagation = BeliefPropagation(self.bayesian_model) query_result = belief_propagation.query(['Q', 'J']) np_test.assert_array_almost_equal(query_result['J'].values, np.array([0.416, 0.584])) np_test.assert_array_almost_equal(query_result['Q'].values, np.array([0.4912, 0.5088]))
def test_map_query_with_evidence(self): belief_propagation = BeliefPropagation(self.bayesian_model) map_query = belief_propagation.map_query(['A', 'R', 'L'], { 'J': 0, 'Q': 1, 'G': 0 }) self.assertDictEqual(map_query, {'A': 1, 'R': 0, 'L': 0})
def test_query_single_variable_with_evidence(self): belief_propagation = BeliefPropagation(self.bayesian_model) query_result = belief_propagation.query(variables=['J'], evidence={ 'A': 0, 'R': 1 }) np_test.assert_array_almost_equal(query_result['J'].values, np.array([0.60, 0.40]))
def test_map_query(self): belief_propagation = BeliefPropagation(self.bayesian_model) map_query = belief_propagation.map_query() self.assertDictEqual(map_query, { 'A': 1, 'R': 1, 'J': 1, 'Q': 1, 'G': 0, 'L': 0 })
def test_query_multiple_variable_with_evidence(self): belief_propagation = BeliefPropagation(self.bayesian_model) query_result = belief_propagation.query(variables=['J', 'Q'], evidence={ 'A': 0, 'R': 0, 'G': 0, 'L': 1 }) np_test.assert_array_almost_equal(query_result['J'].values, np.array([0.818182, 0.181818])) np_test.assert_array_almost_equal(query_result['Q'].values, np.array([0.772727, 0.227273]))
def test_max_calibrate_sepset_belief(self): belief_propagation = BeliefPropagation(self.junction_tree) belief_propagation.max_calibrate() sepset_belief = belief_propagation.get_sepset_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_B = (phi1 * (phi3.maximize(['D'], inplace=False) * phi2).maximize( ['C'], inplace=False)).maximize(['A'], inplace=False) b_C = (phi2 * (phi1.maximize(['A'], inplace=False) * phi3.maximize(['D'], inplace=False))).maximize( ['B'], inplace=False) np_test.assert_array_almost_equal( sepset_belief[frozenset((('A', 'B'), ('B', 'C')))].values, b_B.values) np_test.assert_array_almost_equal( sepset_belief[frozenset((('B', 'C'), ('C', 'D')))].values, b_C.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)
def backward_inference(self, variables, evidence=None): """ Backward inference method using belief propagation. Parameters: ---------- variables: list list of variables for which you want to compute the probability evidence: dict a dict key, value pair as {var: state_of_var_observed} None if no evidence Examples: -------- >>> from pgm.factors.discrete import TabularCPD >>> from pgm.models import DynamicBayesianNetwork as DBN >>> from pgm.inference import DBNInference >>> dbnet = DBN() >>> dbnet.add_edges_from([(('Z', 0), ('X', 0)), (('X', 0), ('Y', 0)), ... (('Z', 0), ('Z', 1))]) >>> z_start_cpd = TabularCPD(('Z', 0), 2, [[0.5, 0.5]]) >>> x_i_cpd = TabularCPD(('X', 0), 2, [[0.6, 0.9], ... [0.4, 0.1]], ... evidence=[('Z', 0)], ... evidence_card=2) >>> y_i_cpd = TabularCPD(('Y', 0), 2, [[0.2, 0.3], ... [0.8, 0.7]], ... evidence=[('X', 0)], ... evidence_card=2) >>> z_trans_cpd = TabularCPD(('Z', 1), 2, [[0.4, 0.7], ... [0.6, 0.3]], ... evidence=[('Z', 0)], ... evidence_card=2) >>> dbnet.add_cpds(z_start_cpd, z_trans_cpd, x_i_cpd, y_i_cpd) >>> dbnet.initialize_initial_state() >>> dbn_inf = DBNInference(dbnet) >>> dbn_inf.backward_inference([('X', 0)], {('Y', 0):0, ('Y', 1):1, ('Y', 2):1})[('X', 0)].values array([ 0.66594382, 0.33405618]) """ variable_dict = defaultdict(list) for var in variables: variable_dict[var[1]].append(var) time_range = max(variable_dict) interface_nodes_dict = {} if evidence: evid_time_range = max( [time_slice for var, time_slice in evidence.keys()]) time_range = max(time_range, evid_time_range) end_bp = BeliefPropagation(self.start_junction_tree) potential_dict = self.forward_inference(variables, evidence, 'potential') update_factor = self._shift_factor(potential_dict[time_range], 1) factor_values = {} for time_slice in range(time_range, 0, -1): evidence_time = self._get_evidence(evidence, time_slice, 1) evidence_prev_time = self._get_evidence(evidence, time_slice - 1, 0) if evidence_prev_time: interface_nodes_dict = { k: v for k, v in evidence_prev_time.items() if k in self.interface_nodes_0 } if evidence_time: evidence_time.update(interface_nodes_dict) mid_bp = BeliefPropagation(self.one_and_half_junction_tree) self._update_belief(mid_bp, self.in_clique, potential_dict[time_slice - 1]) forward_factor = self._shift_factor(potential_dict[time_slice], 1) self._update_belief(mid_bp, self.out_clique, forward_factor, update_factor) if variable_dict[time_slice]: variable_time = self._shift_nodes(variable_dict[time_slice], 1) new_values = mid_bp.query(variable_time, evidence=evidence_time) changed_values = {} for key in new_values.keys(): new_key = (key[0], time_slice) new_factor = DiscreteFactor([new_key], new_values[key].cardinality, new_values[key].values) changed_values[new_key] = new_factor factor_values.update(changed_values) clique_phi = self._get_factor(mid_bp, evidence_time) in_clique_phi = self._marginalize_factor(self.interface_nodes_0, clique_phi) update_factor = self._shift_factor(in_clique_phi, 1) out_clique_phi = self._shift_factor(update_factor, 0) self._update_belief(end_bp, self.start_interface_clique, potential_dict[0], out_clique_phi) evidence_0 = self._get_evidence(evidence, 0, 0) if variable_dict[0]: factor_values.update(end_bp.query(variable_dict[0], evidence_0)) return factor_values