def main():
"""
Main functiont to lunch the belief propagation algorithm
"""
M = model()
M.check_model()
#Belief propagation
bp = BeliefPropagation(M)
bp.calibrate()
print("maximal cliques are:")
print(bp.get_cliques())
# first query
print("computing probability of B=")
query1 = bp.query(variables=list('b'), show_progress=True)
print(query1)
#second query
print("computing probability of B|C")
query2 = bp.query(variables=['b', 'c'])
query2.marginalize(['c'])
print(query2)
#Third query
print("computing joint")
query3 = bp.query(['a', 'b', 'c', 'd', 'e'])
query3.normalize()
print(query3)
def belief_propagation(evidence: dict, bn: BayesianNetwork):
"""
evidence: {node: evidence_value, ...}
bn : our own bayesian network class
"""
network = convert2pgm(bn)
net_infer = BeliefPropagation(network)
to_infer = list(set(network.nodes()) - set(evidence.keys()))
prior = {}
prior_dist = net_infer.query(variables=to_infer, evidence={}, joint=False)
for factor in prior_dist.values():
node = factor.variables[0]
values = factor.values.tolist()
prior[factor.variables[0]] = pd.DataFrame({
node: [0, 1],
"prob": values
})
post = {}
post_dist = net_infer.query(variables=to_infer,
evidence=evidence,
joint=False)
for factor in post_dist.values():
node = factor.variables[0]
values = factor.values.tolist()
post[factor.variables[0]] = pd.DataFrame({
node: [0, 1],
"prob": values
})
return prior, post
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_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_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_query_single_variable(self):
belief_propagation = BeliefPropagation(self.bayesian_model)
query_result = belief_propagation.query(["J"])
self.assertEqual(
query_result,
DiscreteFactor(variables=["J"],
cardinality=[2],
values=[0.416, 0.584]),
)
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_query_multiple_variable(self):
belief_propagation = BeliefPropagation(self.bayesian_model)
query_result = belief_propagation.query(["Q", "J"])
self.assertEqual(
query_result,
DiscreteFactor(
variables=["J", "Q"],
cardinality=[2, 2],
values=np.array([[0.3744, 0.0416], [0.1168, 0.4672]]),
),
)
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
})
self.assertEqual(
query_result,
DiscreteFactor(variables=["J"],
cardinality=[2],
values=np.array([0.072, 0.048])),
)
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_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
})
self.assertEqual(
query_result,
DiscreteFactor(
variables=["J", "Q"],
cardinality=[2, 2],
values=np.array([[0.003888, 0.000432], [0.000192, 0.000768]]),
),
)
def step(self, adjustment, episode):
print('######## Ajustes ########')
print(adjustment)
print('######## Episódio atual ########')
print(episode)
bp = BeliefPropagation(self.model)
replaced_episode = {k: replacer[k][v] for k, v in episode.iteritems()}
upper_bound = self.state[0] + adjustment
lower_bound = self.state[1] - adjustment
if not (upper_bound > 1 or upper_bound < 0):
state_aware = [upper_bound, lower_bound]
cpds = self._tabular_cpds_to_dict(self.model)
adjustments = self.fit_probabilities(cpds, adjustment)
for node in self.model.get_cpds():
if node.variable != 'Consciente':
node.values = self._get_cpd_values(
adjustments[node.variable])
node.normalize()
else:
node.values = np.array(state_aware)
for node in self.model.get_cpds():
print(node)
else:
state_aware = [self.state]
print('######## Consciente ########')
bp = BeliefPropagation(self.model)
print(
bp.query(['Consciente'], evidence=replaced_episode)['Consciente'])
reward = float(input('Recompensa entre -1 e 1: '))
next_state = []
next_state.append(np.round(state_aware, 2))
next_state.extend(list(replaced_episode.values()))
return next_state, reward
def _get_ev(self, dec_instantiation: Tuple[int], row: int,
bp: BeliefPropagation) -> float:
"""Return the expected value of a certain decision node instantiation
for the agent making the decision"""
macid = self.copy_without_cpds()
dec_list = macid.get_valid_acyclic_dec_node_ordering()
dec = dec_list[row]
agent = self.whose_node[dec] # gets the agent making that decision
utils = self.utility_nodes_agent[
agent] # gets the utility nodes for that agent
factor = bp.query(variables=utils,
evidence=dict(zip(dec_list, dec_instantiation)))
ev = 0
for idx, prob in np.ndenumerate(factor.values):
for i in range(
len(utils)
): # account for each agent having multiple utilty nodes
if prob != 0:
ev += prob * idx[i]
return ev
values=[[0.01], [0.99]])
cpd_do = TabularCPD(variable='dog_out',
variable_card=2,
values=[[0.99, 0.9, 0.97, 0.3], [0.01, 0.1, 0.03, 0.7]],
evidence=['family_out', 'bowel_problem'],
evidence_card=[2, 2])
cpd_lo = TabularCPD(variable='light_on',
variable_card=2,
values=[[0.6, 0.05], [0.4, 0.95]],
evidence=['family_out'],
evidence_card=[2])
cpd_hb = TabularCPD(variable='hear_bark',
variable_card=2,
values=[[0.7, 0.01], [0.3, 0.99]],
evidence=['dog_out'],
evidence_card=[2])
#integrity checking
model.add_cpds(cpd_fo, cpd_bp, cpd_do, cpd_lo, cpd_hb)
model.check_model()
junction_tree = model.to_junction_tree()
print(junction_tree.nodes())
infer_bp = BeliefPropagation(junction_tree)
print(
infer_bp.query(['family_out'], evidence={
'light_on': 0,
'hear_bark': 1
})['family_out'])
def compute_pk(self, type_list, fid):
assert len(type_list) == 5, print("ComputePk Error: number of type_list should be 5")
constraint_name = ['m', 'r', 's', 'd', 'v']
'''
m, r, s, d, v = type_list
p_m, p_r, p_s, p_d, p_v = self.p_observation
p_ktox, p_xtok = self.p_implication
p_ktom, p_ktor, p_ktos, p_ktod, p_ktov = p_ktox
p_mtok, p_rtok, p_stok, p_dtok, p_vtok = p_xtok
'''
fg = FactorGraph()
fg.add_node('k')
for i in range(len(type_list)):
if type_list[i] == 0:
fg = self.add_constraints_k2x_x2k(fg, self.p_observation[fid][i], self.p_implication[fid][0][i], self.p_implication[fid][1][i], constraint_name[i])
elif type_list[i] == 1:
fg = self.add_constraints_k2x(fg, self.p_observation[fid][i], self.p_implication[fid][0][i], constraint_name[i])
elif type_list[i] == 2:
fg = self.add_constraints_x2k(fg, self.p_observation[fid][i], self.p_implication[fid][1][i], constraint_name[i])
'''
if m == 0:
fg = add_constraints_kv_vk(fg, p_m, p_ktom, p_mtok, 'm')
elif m == 1:
fg = add_constraints_kv(fg, p_m, p_mtok, 'm')
elif m == 2:
fg = add_constraints_vk(fg, p_m, p_mtok, 'm')
if r == 0:
fg = add_constraints_kv_vk(fg, p_r, p_ktor, p_rtok, 'r')
elif r == 1:
fg = add_constraints_kv(fg, p_r, p_ktor, 'r')
elif r == 2:
fg = add_constraints_vk(fg, p_r, p_rtok, 'r')
if s == 0:
fg = add_constraints_kv_vk(fg, p_s, p_ktos, p_stok, 's')
elif s == 1:
fg = add_constraints_kv(fg, p_s, p_ktos, 's')
elif s == 2:
fg = add_constraints_vk(fg, p_s, p_stok, 's')
if d == 0:
fg = add_constraints_kv_vk(fg, p_d, p_ktod, p_dtok, 'd')
elif d == 1:
fg = add_constraints_kv(fg, p_d, p_ktod, 'd')
elif d == 2:
fg = add_constraints_vk(fg, p_d, p_dtok, 'd')
if v == 0:
fg = add_constraints_kv_vk(fg, p_v, p_ktov, p_vtok, 'v')
elif v == 1:
fg = add_constraints_kv(fg, p_v, p_ktov, 'v')
elif v == 2:
fg = add_constraints_vk(fg, p_v, p_vtok, 'v')
'''
bp = BeliefPropagation(fg)
#result = bp.query(variables=['k'])['k']
#result = bp.query(variables=['k'], joint=False)['k']
result = bp.query(variables=['k'])
result.normalize()
#print(result)
return result.values[1]
PGM.add_edges_from([('w1', 'w2'), ('w2', 'w3')])
tr_matrix = np.array([1, 10, 3, 2, 1, 5, 3, 3, 2])
tr_matrix = np.array([1, 2, 3, 10, 1, 3, 3, 5, 2]).reshape(3, 3).T.reshape(-1)
phi = [DiscreteFactor(edge, [3, 3], tr_matrix) for edge in PGM.edges()]
print(phi[0])
print(phi[1])
PGM.add_factors(*phi)
# Calculate partition funtion
Z = PGM.get_partition_function()
print('The partition function is:', Z)
# Calibrate the click
belief_propagation = BeliefPropagation(PGM)
belief_propagation.calibrate()
# Output calibration result, which you should get
query = belief_propagation.query(variables=['w2'])
print('After calibration you should get the following mu(S):\n', query * Z)
# Get marginal distribution over third word
query = belief_propagation.query(variables=['w3'])
print('Marginal distribution over the third word is:\n', query)
#Get conditional distribution over third word
query = belief_propagation.query(variables=['w3'],
evidence={'w1': 0}) # 0 stays for "noun"
print(
'Conditional distribution over the third word, given that the first word is noun is:\n',
query)
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 pgmpy.factors import TabularCPD
>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> from pgmpy.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 = Factor([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
#------------------Calculate inference using Mplp algorithm--------------------
mplp = Mplp(mark)
mplp.find_triangles()
mplp.map_query()
#infer1 = BayesianModelSampling(mark)
#evidence1 = [State('y',1)]
#sample1 = infer1.forward_sample(5)
#sample1
#---------Calculate inference using Belief Propagation and Variable Elimination and answer corresponding queries-------------
belief_prop = BeliefPropagation(mark)
bp1 = belief_prop.query(variables=['y'], evidence={'marital': 2, 'default': 0})
print(bp1['y'])
infer = VariableElimination(mark)
phi_query = infer.query(variables=['y'], evidence={'marital': 0, 'default': 0})
print(bp1['y'])
bp2 = belief_prop.query(variables=['y'],
evidence={
'education': 2,
'housing': 1
})
print(bp2['y'])
infer = VariableElimination(mark)
phi_query = infer.query(variables=['y'],
columns=['A', 'B', 'C', 'D', 'E'])
print(values)
model = BayesianModel([('A', 'B'), ('C', 'B'), ('C', 'D'), ('B', 'E')])
model.fit(values)
ve = VariableElimination(model)
bp = BeliefPropagation(model)
start = time.time()
ve_result = ve.query(['B'], evidence={'A': 0}) #, 'B'])
end = time.time()
print(ve_result['B'])
print("time: {}".format(end - start))
start = time.time()
bp_result = bp.query(['B'], evidence={'A': 0})
'''
if 'B' in bp_result:
if 'B_0' in bp_result['B']:
print("yes")
else:
print("no")
'''
print(bp_result['B'].variables)
print(bp_result['B'].values)
'''for key, value in bp_result.items():
print value.keys()[0]
'''
'''
end = time.time()
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]))
train = data[1:600]
x = Mental_health_model.fit(train, estimator=MaximumLikelihoodEstimator)
#for cpd in Mental_health_model.get_cpds():
# print(cpd)
# In[2]:
# In[3]:
belief_prop = BeliefPropagation(Mental_health_model)
# In[5]:
bp1 = belief_prop.query(variables=['leave', 'wellness_program'],
evidence={'tech_company': 0})
print(bp1['leave'])
print(bp1['wellness_program'])
# In[6]:
bp2 = belief_prop.query(variables=['treatment'],
evidence={
'Age': 1,
'Gender': 0,
'family_history': 1
})
print(bp2['treatment'])
# In[7]:
def markov_inference(dict_of_esp_jointprob):
"""Calculate the markov model """
factor_mmb_cmma = Factor(variables=['money_market_bonus', 'collateral_mma'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['mmb0_cmma0'], dict_of_esp_jointprob['mmb0_cmma1'],
dict_of_esp_jointprob['mmb1_cmma0'], dict_of_esp_jointprob['mmb1_cmma1']])
factor_mmb_cm = Factor(variables=['money_market_bonus', 'cash_management'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['mmb0_cm0'], dict_of_esp_jointprob['mmb0_cm1'],
dict_of_esp_jointprob['mmb1_cm0'], dict_of_esp_jointprob['mmb1_cm1']])
factor_mmb_fx = Factor(variables=['money_market_bonus', 'fx_products'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['mmb0_fx0'], dict_of_esp_jointprob['mmb0_fx1'],
dict_of_esp_jointprob['mmb1_fx0'], dict_of_esp_jointprob['mmb1_fx1']])
factor_mmb_loc = Factor(variables=['money_market_bonus', 'letters_of_credit'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['mmb0_loc0'], dict_of_esp_jointprob['mmb0_loc1'],
dict_of_esp_jointprob['mmb1_loc0'], dict_of_esp_jointprob['mmb1_loc1']])
factor_mmb_es = Factor(variables=['money_market_bonus', 'enterprise_sweep'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['mmb0_es0'], dict_of_esp_jointprob['mmb0_es1'],
dict_of_esp_jointprob['mmb1_es0'], dict_of_esp_jointprob['mmb1_es1']])
factor_mmb_checking = Factor(variables=['money_market_bonus', 'checking_usd'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['mmb0_checking0'], dict_of_esp_jointprob['mmb0_checking1'],
dict_of_esp_jointprob['mmb1_checking0'], dict_of_esp_jointprob['mmb1_checking1']])
# collateral mma
factor_cmma_cm = Factor(variables=['collateral_mma','cash_management'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['cmma0_cm0'], dict_of_esp_jointprob['cmma0_cm1'],
dict_of_esp_jointprob['cmma1_cm0'], dict_of_esp_jointprob['cmma1_cm1']])
factor_cmma_fx = Factor(variables=['collateral_mma', 'fx_products'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['cmma0_fx0'], dict_of_esp_jointprob['cmma0_fx1'],
dict_of_esp_jointprob['cmma1_fx0'], dict_of_esp_jointprob['cmma1_fx1']])
factor_cmma_loc = Factor(variables=['collateral_mma', 'letters_of_credit'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['cmma0_loc0'], dict_of_esp_jointprob['cmma0_loc1'],
dict_of_esp_jointprob['cmma1_loc0'], dict_of_esp_jointprob['cmma1_loc1']])
factor_cmma_es= Factor(variables=['collateral_mma', 'enterprise_sweep'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['cmma0_es0'], dict_of_esp_jointprob['cmma0_es1'],
dict_of_esp_jointprob['cmma1_es0'], dict_of_esp_jointprob['cmma1_es1']])
factor_cmma_checking = Factor(variables=['collateral_mma', 'checking_usd'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['cmma0_checking0'], dict_of_esp_jointprob['cmma0_checking1'],
dict_of_esp_jointprob['cmma1_checking0'],dict_of_esp_jointprob['cmma1_checking1']])
# cash management
factor_cm_fx = Factor(variables=['cash_management', 'fx_products'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['cm0_fx0'], dict_of_esp_jointprob['cm0_fx1'],
dict_of_esp_jointprob['cm1_fx0'], dict_of_esp_jointprob['cm1_fx1']])
factor_cm_loc = Factor(variables=['cash_management', 'letters_of_credit'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['cm0_loc0'], dict_of_esp_jointprob['cm0_loc1'],
dict_of_esp_jointprob['cm1_loc0'], dict_of_esp_jointprob['cm1_loc1']])
factor_cm_es= Factor(variables=['cash_management', 'enterprise_sweep'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['cm0_es0'], dict_of_esp_jointprob['cm0_es1'],
dict_of_esp_jointprob['cm1_es0'], dict_of_esp_jointprob['cm1_es1']])
factor_cm_checking = Factor(variables=['cash_management', 'checking_usd'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['cm0_checking0'], dict_of_esp_jointprob['cm0_checking1'],
dict_of_esp_jointprob['cm1_checking0'], dict_of_esp_jointprob['cm1_checking1']])
# FX products
factor_fx_loc = Factor(variables=['fx_products', 'letters_of_credit'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['fx0_loc0'], dict_of_esp_jointprob['fx0_loc1'],
dict_of_esp_jointprob['fx1_loc0'], dict_of_esp_jointprob['fx1_loc1']])
factor_fx_es= Factor(variables=['fx_products', 'enterprise_sweep'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['fx0_es0'], dict_of_esp_jointprob['fx0_es1'],
dict_of_esp_jointprob['fx1_es0'], dict_of_esp_jointprob['fx1_es1']])
factor_fx_checking = Factor(variables=['fx_products', 'checking_usd'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['fx0_checking0'], dict_of_esp_jointprob['fx0_checking1'],
dict_of_esp_jointprob['fx1_checking0'], dict_of_esp_jointprob['fx1_checking1']])
# letters of credit
factor_loc_es= Factor(variables=['letters_of_credit', 'enterprise_sweep'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['loc0_es0'], dict_of_esp_jointprob['loc0_es1'],
dict_of_esp_jointprob['loc1_es0'], dict_of_esp_jointprob['loc1_es1']])
factor_loc_checking = Factor(variables=['letters_of_credit', 'checking_usd'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['loc0_checking0'], dict_of_esp_jointprob['loc0_checking1'],
dict_of_esp_jointprob['loc1_checking0'], dict_of_esp_jointprob['loc1_checking1']])
#enterprise sweep
factor_es_checking = Factor(variables=['enterprise_sweep', 'checking_usd'],
cardinality=[2, 2],
values=[dict_of_esp_jointprob['es0_checking0'], dict_of_esp_jointprob['es0_checking1'],
dict_of_esp_jointprob['es1_checking0'], dict_of_esp_jointprob['es1_checking1']])
# built the markov model
model.add_factors(factor_mmb_cmma , factor_mmb_cm, factor_mmb_fx, factor_mmb_loc,factor_mmb_es, factor_mmb_checking,
factor_cmma_cm , factor_cmma_fx, factor_cmma_loc, factor_cmma_es,factor_cmma_checking,
factor_cm_fx, factor_cm_loc, factor_cm_es, factor_cm_checking , factor_fx_loc,
factor_fx_es , factor_fx_checking, factor_loc_es, factor_loc_checking , factor_es_checking )
belief_propagation = BeliefPropagation(model)
all_products = ['money_market_bonus','collateral_mma', 'cash_management','enterprise_sweep',
'fx_products','letters_of_credit','checking_usd']
# perform inference for all product except the one in the for loop
for prod in all_products:
if evidence_==None:
new_evidence=evidence_
else:
new_evidence = {key: value for key, value in evidence_.items()
if key != prod}
# perform belief inference on only one product at a time
belief_inference_products = str(prod)
# belief propogation on one product at a time given evidence from all other products
belief = belief_propagation.query(variables=[belief_inference_products], evidence=new_evidence)
try:
#mmb = belief_mmb['money_market_bonus'].values[1]
mmb = belief['money_market_bonus'].values[1]
if mmb <0 :
mmb = .0000001
elif mmb >1:
mmb =1
prob_mmb.append(mmb)# one is having the product
except: # can't perform inference on this product
pass
try:
cmma = belief['collateral_mma'].values[1]
if cmma <0:
cmma = .0000001
elif cmma >1:
cmma =1
prob_cmma.append(cmma)
except:## don't have this product
pass
try:
cm = belief['cash_management'].values[1]
if cm <0:
cm = .0000001
elif cm >1:
cm =1
prob_cm.append(cm)
except:
pass
try:
checking = belief['checking_usd'].values[1]
if checking <0:
checking = .0000001
elif checking >1:
checking =1
prob_checking.append(checking)
except:
pass
try:
fx = belief['fx_products'].values[1]
if fx <0:
fx = .0000001
elif fx >1:
fx =1
prob_fx.append(fx)
except:
pass
try:
loc = belief['letters_of_credit'].values[1]
if loc <0:
loc = .0000001
elif loc > 1:
loc = 1
prob_loc.append(loc)
except:
pass
try:
es = belief['enterprise_sweep'].values[1]
if es<0:
es = .0000001
elif es >1:
es = 1
prob_es.append(es)
except:
pass
def plot_causal_influence(self, file_path):
"""
Computes the odds of the target variable being value 1 over value 0 (i.e. the odds ratio)
by iterating through all other network variables/nodes, changing their values,
and observing how the probability of the target variable changes. Belief propagation
is used for inference. A forest plot is produced from this and saved to disk.
Arguments:
file_path: str, the absolute path to save the file to (e.g. "~/Desktop/forest_plot.png")
Returns:
None
"""
# Estimate CPTs
self._estimate_CPT()
if self.verbose:
print(f"Calculating influence of all nodes on target node")
if not self.bn_model.check_model():
print("""
There is a problem with your network structure. You have disconnected nodes
or separated sub-networks. Please examine your network plot and re-learn your
network structure with tweaked settings.
""")
return None
if self.target_variable not in self.bn_model.nodes:
print("""
Your target variable has no parent nodes! Can't perform inference! Please examine
your network plot and re-learn your network structure with tweaked settings.
""")
return None
# Prep for belief propagation
belief_propagation = BeliefPropagation(self.bn_model)
belief_propagation.calibrate()
# Iterate over all intervention nodes and values, calculating odds ratios w.r.t target variable
overall_dict = {}
variables_to_test = list(
set(list(self.bn_model.nodes)) - set(list(self.target_variable)))
for node in variables_to_test:
results = []
for value in self.filtered_df[node].unique():
prob = belief_propagation.query(
variables=[self.target_variable],
evidence={
node: value
},
show_progress=False,
).values
results.append([node, value, prob[0], prob[1]])
results_df = pd.DataFrame(
results,
columns=["node", "value", "probability_0", "probability_1"])
results_df["odds_1"] = (results_df["probability_1"] /
results_df["probability_0"])
results_df = results_df.sort_values(
"value", ascending=True, inplace=False).reset_index(drop=True)
overall_dict[node] = results_df
final_df_list = []
for node, temp_df in overall_dict.items():
first_value = temp_df["odds_1"].iloc[0]
temp_df["odds_ratio"] = (temp_df["odds_1"] / first_value).round(3)
final_df_list.append(temp_df)
final_df = pd.concat(final_df_list)[["node", "value", "odds_ratio"]]
self.odds_ratios = final_df
if self.verbose:
print(f"Saving forest plot to the following PNG file: {file_path}")
# Clean up the dataframe of odds ratios so plot can have nice labels
final_df2 = (pd.concat([
final_df,
final_df.groupby("node")["value"].apply(
lambda x: x.shift(-1).iloc[-1]).reset_index(),
]).sort_values(by=["node", "value"],
ascending=True).reset_index(drop=True))
final_df2["node"][final_df2["value"].isnull()] = np.nan
final_df2["value"] = final_df2["value"].astype("Int32").astype(str)
final_df2["value"].replace({np.nan: ""}, inplace=True)
final_df3 = final_df2.reset_index(drop=True).reset_index()
final_df3.rename(columns={"index": "vertical_index"}, inplace=True)
final_df3["y_label"] = final_df3["node"] + " = " + final_df3["value"]
final_df3["y_label"][final_df3["odds_ratio"] == 1.0] = (
final_df3["y_label"] + " (ref)")
final_df3["y_label"].fillna("", inplace=True)
# Produce large plot
plt.clf()
plt.title(
"Strength of Associations Between Interventions and Target Variable"
)
plt.scatter(
x=final_df3["odds_ratio"],
y=final_df3["vertical_index"],
s=70,
color="b",
alpha=0.5,
)
plt.xlabel("Odds Ratio")
plt.axvline(x=1.0, color="red", linewidth="1.5", linestyle="--")
plt.yticks(final_df3["vertical_index"], final_df3["y_label"])
for _, row in final_df3.iterrows():
if not np.isnan(row["odds_ratio"]):
plt.plot(
[0, row["odds_ratio"]],
[row["vertical_index"], row["vertical_index"]],
color="black",
linewidth="0.4",
)
plt.xlim([0, final_df3["odds_ratio"].max() + 1])
figure = plt.gcf()
figure.set_size_inches(12, 7)
plt.savefig(expanduser(file_path),
bbox_inches="tight",
format="PNG",
dpi=300)
PGM.add_nodes_from(['w1', 'w2', 'w3'])
PGM.add_edges_from([('w1', 'w2'), ('w2', 'w3')])
tr_matrix = np.array([1, 2, 3, 10, 1, 3, 3, 5, 2]).reshape(3, 3).T.reshape(-1)
phi = [DiscreteFactor(edge, [3, 3], tr_matrix) for edge in PGM.edges()]
PGM.add_factors(*phi)
# Calculate partition funtion
Z = PGM.get_partition_function()
print('The partition function is:', Z)
# Calibrate the click
belief_propagation = BeliefPropagation(PGM)
belief_propagation.calibrate()
# Output calibration result, which you should get
query = belief_propagation.query(variables=["w2"], joint=False)
print('After calibration you should get the following mu(S):', query["w2"] * Z)
# Get marginal distribution over third word
query = belief_propagation.query(variables=['w3'],
joint=False) #, evidence = {'w2':0})
print('Marginal distribution over the third word is:\n', query["w3"])
#Get conditional distribution over third word
query = belief_propagation.query(variables=['w3'],
evidence={'w1': 0},
joint=False) # 0 stays for "noun"
print(
'Conditional distribution over the third word, given that the first word is noun is:\n',
query["w3"])
def time_query_alarm(self):
infer = BeliefPropagation(self.alarm)
infer.query(variables=['VENTLUNG'])
########################################################################
model = BayesianModel([('class', 'doors'), ('class', 'safety'),
('class', 'maint'), ('class', 'buying'),
('class', 'persons'), ('class', 'lug_boot')])
model.fit(df_train, estimator=MaximumLikelihoodEstimator)
# print(model.get_cpds('class').values)
# print(model.active_trail_nodes('doors', observed='class'))
# can also use Belief propagation #
inference = BeliefPropagation(model)
print("Class variable prior:\n{}\n".format(
inference.query(variables=['class'])['class']))
print("Class variable posterior after certain observation:\n{}\n".format(
inference.query(variables=['class'], evidence={'doors': 0})['class']))
#####################
# Predict test data #
#####################
predict_data = df_test.copy()
predict_data.drop(['class'], axis=1, inplace=True)
# y_pred = model.predict(predict_data)
pred_values = []
for index, data_point in predict_data.iterrows():
prob_dist = inference.query(variables=['class'],
evidence=data_point.to_dict())['class'].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 pgmpy.factors.discrete import TabularCPD
>>> from pgmpy.models import DynamicBayesianNetwork as DBN
>>> from pgmpy.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
model.add_cpds(..........)
# Apply propagation
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()
# To get the sepset beliefs use the corresponding getters
belief_propagation.get_sepset_beliefs()
>> # Query variables not in the same cluster
belief_propagation.query(variables=['no_of_people'], evidence={'location':1, 'quality':1})
>> # Can apply MAP_Query - next
belief_propagation.map_query(variables=['no_of_people'], evidence={'location':1, 'quality':1})
" {'no_of_people': 0} "
-4- " MAP - Maximize A Posterior Probability "
" Given the current states to find out the maximized predicted var state - prediction "
" Different from Query which only care find out the distribution of target var over all states "