Bayesian Belief Network is created using pgmpy and some simple queries are done on the network. This network is an Alarm Byaesian Beleief Network which is mentioned in Bayesian Artificial Intelligence - Section 2.5.1 (https://bayesian-intelligence.com/publications/bai/book/BAI_Chapter2.pdf)



In [9]:

    
#Importing Library
from pgmpy.models import BayesianModel
from pgmpy.inference import VariableElimination



In [10]:

    
#Defining network structure

alarm_model = BayesianModel([('Burglary', 'Alarm'), 
                              ('Earthquake', 'Alarm'),
                              ('Alarm', 'JohnCalls'),
                              ('Alarm', 'MaryCalls')])

#Defining the parameters using CPT
from pgmpy.factors.discrete import TabularCPD

cpd_burglary = TabularCPD(variable='Burglary', variable_card=2,
                      values=[[.999], [0.001]])
cpd_earthquake = TabularCPD(variable='Earthquake', variable_card=2,
                       values=[[0.998], [0.002]])
cpd_alarm = TabularCPD(variable='Alarm', variable_card=2,
                        values=[[0.999, 0.71, 0.06, 0.05],
                                [0.001, 0.29, 0.94, 0.95]],
                        evidence=['Burglary', 'Earthquake'],
                        evidence_card=[2, 2])
cpd_johncalls = TabularCPD(variable='JohnCalls', variable_card=2,
                      values=[[0.95, 0.1], [0.05, 0.9]],
                      evidence=['Alarm'], evidence_card=[2])
cpd_marycalls = TabularCPD(variable='MaryCalls', variable_card=2,
                      values=[[0.1, 0.7], [0.9, 0.3]],
                      evidence=['Alarm'], evidence_card=[2])

# Associating the parameters with the model structure
alarm_model.add_cpds(cpd_burglary, cpd_earthquake, cpd_alarm, cpd_johncalls, cpd_marycalls)



In [11]:

    
# Checking if the cpds are valid for the model
alarm_model.check_model()









    Out[11]:





True



In [12]:

    
# Viewing nodes of the model
alarm_model.nodes()









    Out[12]:





NodeView(('Burglary', 'Alarm', 'Earthquake', 'JohnCalls', 'MaryCalls'))



In [13]:

    
# Viewing edges of the model
alarm_model.edges()









    Out[13]:





OutEdgeView([('Burglary', 'Alarm'), ('Alarm', 'JohnCalls'), ('Alarm', 'MaryCalls'), ('Earthquake', 'Alarm')])



In [15]:

    
#Checking independcies of a node
alarm_model.local_independencies('Burglary')









    Out[15]:





(Burglary _|_ Earthquake)



In [16]:

    
#Listing all Independencies
alarm_model.get_independencies()









    Out[16]:





(Burglary _|_ Earthquake)
(Burglary _|_ MaryCalls, JohnCalls | Alarm)
(Burglary _|_ JohnCalls | MaryCalls, Alarm)
(Burglary _|_ MaryCalls, JohnCalls | Alarm, Earthquake)
(Burglary _|_ MaryCalls | JohnCalls, Alarm)
(Burglary _|_ JohnCalls | MaryCalls, Alarm, Earthquake)
(Burglary _|_ MaryCalls | Alarm, JohnCalls, Earthquake)
(Earthquake _|_ Burglary)
(Earthquake _|_ MaryCalls, JohnCalls | Alarm)
(Earthquake _|_ MaryCalls, JohnCalls | Burglary, Alarm)
(Earthquake _|_ JohnCalls | MaryCalls, Alarm)
(Earthquake _|_ MaryCalls | JohnCalls, Alarm)
(Earthquake _|_ JohnCalls | Burglary, MaryCalls, Alarm)
(Earthquake _|_ MaryCalls | Burglary, JohnCalls, Alarm)
(JohnCalls _|_ Burglary, MaryCalls, Earthquake | Alarm)
(JohnCalls _|_ MaryCalls, Earthquake | Burglary, Alarm)
(JohnCalls _|_ Burglary, Earthquake | MaryCalls, Alarm)
(JohnCalls _|_ Burglary, MaryCalls | Alarm, Earthquake)
(JohnCalls _|_ Earthquake | Burglary, MaryCalls, Alarm)
(JohnCalls _|_ MaryCalls | Burglary, Alarm, Earthquake)
(JohnCalls _|_ Burglary | MaryCalls, Alarm, Earthquake)
(MaryCalls _|_ Burglary, JohnCalls, Earthquake | Alarm)
(MaryCalls _|_ JohnCalls, Earthquake | Burglary, Alarm)
(MaryCalls _|_ Burglary, JohnCalls | Alarm, Earthquake)
(MaryCalls _|_ Burglary, Earthquake | JohnCalls, Alarm)
(MaryCalls _|_ JohnCalls | Burglary, Alarm, Earthquake)
(MaryCalls _|_ Earthquake | Burglary, JohnCalls, Alarm)
(MaryCalls _|_ Burglary | Alarm, JohnCalls, Earthquake)