Description

E09 Bayesian Network

17341015 Hongzheng Chen
Contents
1 Pomegranate Installation 2
2 Building Bayesian Network 2
3 Tasks 3
3.1 Burglary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.2 Diagnosing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4 Codes and Results 6
1 Pomegranate Installation
Under Linux:
1. Install python first (python 2, not python 3).
2. Run sudo apt-get install python-pip to install pip.
3. Run sudo pip install pomegranate to install pomegranate.

Under Windows
You can also run pip install pomegranate if you have installed pip. If you don’t know how to install pip, please click https://jingyan.baidu.com/article/e73e26c0d94e0524adb6a7ff.html.
For more, please click the homepage of Pomegranate – https://github.com/jmschrei/pomegranate for help.

2 Building Bayesian Network
Please refer to Tutorial 4 Bayesian Networks.pdf. I will explain it in class.

3 Tasks
3.1 Burglary
Please code to calculate:
1.
2.
3.
4.
5.
6.

3.2 Diagnosing
Variables and their domais
(1)PatientAge:[’0-30’,’31-65’,’65+’]
(2)CTScanResult:[’Ischemic Stroke’,’Hemmorraghic Stroke’]
(3)MRIScanResult: [’Ischemic Stroke’,’Hemmorraghic Stroke’]
(4)StrokeType: [’Ischemic Stroke’,’Hemmorraghic Stroke’, ’Stroke Mimic’]
(5)Anticoagulants: [’Used’,’Not used’]
(6)Mortality:[’True’, ’False’]
(7)Disability: [’Negligible’, ’Moderate’, ’Severe’]
CPTs
Note: [CTScanResult, MRIScanResult,StrokeType] means:
P(StrokeType=’…’ | CTScanResult=’…’ ∧ MRIScanResult=’…’)
(1)
[PatientAge]
[’0-30’, 0.10],
[’31-65’, 0.30],
[’65+’, 0.60]
(2)
[CTScanResult]
[’Ischemic Stroke’,0.7],
[ ’Hemmorraghic Stroke’,0.3]
(3)
[MRIScanResult]
[’Ischemic Stroke’,0.7],
[ ’Hemmorraghic Stroke’,0.3]
(4)
[Anticoagulants]
[’Used’,0.5],
[’Not used’,0.5]
(5)
[CTScanResult, MRIScanResult,StrokeType]
[’Ischemic Stroke’,’Ischemic Stroke’,’Ischemic Stroke’,0.8],
[’Ischemic Stroke’,’Hemmorraghic Stroke’,’Ischemic Stroke’,0.5],
[ ’Hemmorraghic Stroke’,’Ischemic Stroke’,’Ischemic Stroke’,0.5],
[ ’Hemmorraghic Stroke’,’Hemmorraghic Stroke’,’Ischemic Stroke’,0],
[’Ischemic Stroke’,’Ischemic Stroke’,’Hemmorraghic Stroke’,0],
[’Ischemic Stroke’,’Hemmorraghic Stroke’,’Hemmorraghic Stroke’,0.4],
[ ’Hemmorraghic Stroke’,’Ischemic Stroke’,’Hemmorraghic Stroke’,0.4],
[ ’Hemmorraghic Stroke’,’Hemmorraghic Stroke’,’Hemmorraghic Stroke’,0.9],
[’Ischemic Stroke’,’Ischemic Stroke’,’Stroke Mimic’,0.2],
[’Ischemic Stroke’,’Hemmorraghic Stroke’,’Stroke Mimic’,0.1],
[ ’Hemmorraghic Stroke’,’Ischemic Stroke’,’Stroke Mimic’,0.1],
[ ’Hemmorraghic Stroke’,’Hemmorraghic Stroke’,’Stroke Mimic’,0.1],
(6)
[StrokeType, Anticoagulants, Mortality]
[’Ischemic Stroke’, ’Used’, ’False’,0.28],
[’Hemmorraghic Stroke’, ’Used’, ’False’,0.99],
[’Stroke Mimic’, ’Used’, ’False’,0.1],
[’Ischemic Stroke’,’Not used’, ’False’,0.56],
[’Hemmorraghic Stroke’, ’Not used’, ’False’,0.58],
[’Stroke Mimic’, ’Not used’, ’False’,0.05],
[’Ischemic Stroke’, ’Used’ ,’True’,0.72],
[’Hemmorraghic Stroke’, ’Used’, ’True’,0.01],
[’Stroke Mimic’, ’Used’, ’True’,0.9],
[’Ischemic Stroke’, ’Not used’ ,’True’,0.44],
[’Hemmorraghic Stroke’, ’Not used’, ’True’,0.42 ],
[’Stroke Mimic’, ’Not used’, ’True’,0.95]
(7)
[StrokeType, PatientAge, Disability]
[’Ischemic Stroke’, ’0-30’,’Negligible’, 0.80],
[’Hemmorraghic Stroke’, ’0-30’,’Negligible’, 0.70],
[’Stroke Mimic’, ’0-30’, ’Negligible’,0.9],
[’Ischemic Stroke’, ’31-65’,’Negligible’, 0.60],
[’Hemmorraghic Stroke’, ’31-65’,’Negligible’, 0.50],
[’Stroke Mimic’, ’31-65’, ’Negligible’,0.4],
[’Ischemic Stroke’, ’65+’ , ’Negligible’,0.30],
[’Hemmorraghic Stroke’, ’65+’ , ’Negligible’,0.20], [’Stroke Mimic’, ’65+’ , ’Negligible’,0.1],
[’Ischemic Stroke’, ’0-30’ ,’Moderate’,0.1],
[’Hemmorraghic Stroke’, ’0-30’ ,’Moderate’,0.2],
[’Stroke Mimic’, ’0-30’ ,’Moderate’,0.05],
[’Ischemic Stroke’, ’31-65’,’Moderate’,0.3],
[’Hemmorraghic Stroke’, ’31-65’,’Moderate’,0.4],
[’Stroke Mimic’, ’31-65’,’Moderate’,0.3],
[’Ischemic Stroke’, ’65+’ ,’Moderate’,0.4],
[’Hemmorraghic Stroke’, ’65+’ ,’Moderate’,0.2], [’Stroke Mimic’, ’65+’ ,’Moderate’,0.1],
[’Ischemic Stroke’, ’0-30’ ,’Severe’,0.1],
[’Hemmorraghic Stroke’, ’0-30’ ,’Severe’,0.1],
[’Stroke Mimic’, ’0-30’ ,’Severe’,0.05],
[’Ischemic Stroke’, ’31-65’,’Severe’,0.1],
[’Hemmorraghic Stroke’, ’31-65’,’Severe’,0.1],
[’Stroke Mimic’, ’31-65’,’Severe’,0.3],
[’Ischemic Stroke’, ’65+’ ,’Severe’,0.3],
[’Hemmorraghic Stroke’, ’65+’ ,’Severe’,0.6], [’Stroke Mimic’, ’65+’ ,’Severe’,0.8]
Calculation
Please code to calculate the following probability value:
p1 = P(Mortality=’True’ | PatientAge=’31-65’ ∧ CTScanResult=’Ischemic Stroke’) p2 = P(Disability=’Moderate’ | PatientAge=’65+’ ∧ MRIScanResult=’Hemmorraghic Stroke’) p3 = P(StrokeType=’Stroke Mimic’ | PatientAge=’65+’ ∧ CTScanResult=’Hemmorraghic Stroke’ ∧ MRIScanResult=’Ischemic Stroke’)
p4 = P(Anticoagulants=’Not used’ | PatientAge=’0-30’)

Please solve the 2 tasks and hand in a file named E09 YourNumber.pdf, and send it to ai 201901@foxmail.com
4 Codes and Results
The codes use Python 3!

burglary.py
from pomegranate import *
burglary = DiscreteDistribution( {’T’:0.001, ’F’:0.999} ) earthquake = DiscreteDistribution( {’T’:0.002, ’F’:0.998} ) alarm = ConditionalProbabilityTable(
[[’T’,’T’,’T’,0.95],
[’T’,’F’,’T’,0.94],
[’F’,’T’,’T’,0.29],
[’F’,’F’,’T’,0.001],
[’T’,’T’,’F’,0.05],
[’T’,’F’,’F’,0.06],
[’F’,’T’,’F’,0.71],
[’F’,’F’,’F’,0.999]], [burglary, earthquake]) johncalls = ConditionalProbabilityTable(
[[’T’,’T’,0.90],
[’F’,’T’,0.05],
[’T’,’F’,0.10],
[’F’,’F’,0.95]], [alarm]) marycalls = ConditionalProbabilityTable(
[[’T’,’T’,0.70],
[’F’,’T’,0.01],
[’T’,’F’,0.30],
[’F’,’F’,0.99]], [alarm])
s1 = State(burglary, name=”burglary”) s2 = State(earthquake, name=”earthquake”) s3 = State(alarm, name=”alarm”) s4 = State(johncalls, name=”johncalls”) s5 = State(marycalls, name=”marycalls”)
model = BayesianNetwork(“Burglary”) model.add_states(s1,s2,s3,s4,s5)
model.add_transition(s1,s3) model.add_transition(s2,s3) model.add_transition(s3,s4) model.add_transition(s3,s5) model.bake()
marginals = model.predict_proba({})
# P(A) print(“P(A) = {}”.format(marginals[2].parameters[0][“T”]))
# P(J&&~M) = P(J|~M)P(~M) j_nm = model.predict_proba({’marycalls’:’F’})[3].parameters[0][“T”] * marginals[4].
,→ parameters[0][“F”] print(“P(J && ~M) = {}”.format(j_nm))
# P(A|J&&~M) print(“P(A | J && ~M) = {}”.format(model.predict_proba({’johncalls’:’T’,’marycalls’:’F’}) ,→ [2].parameters[0][“T”]))
# P(B|A) print(“P(B | A) = {}”.format(model.predict_proba({’alarm’:’T’})[0].parameters[0][“T”]))
# P(B|J&&~M) b_c_j_nm = model.predict_proba({’johncalls’:’T’,’marycalls’:’F’})[0].parameters[0][“T”] print(“P(B | J && ~M) = {}”.format(b_c_j_nm)) # P(J&&~M|~B) = P(~B && J && ~M) / P(~B)
# = P(~B | J && ~M) P(J && ~M) / P(~B)
# = (1- P(B | J && ~M)) P(J && ~M) / P(~B)
print(“P(J && ~M | ~B) = {}”.format((1-b_c_j_nm) * j_nm / marginals[0].parameters[0][“F”]))

diagnosing.py
from pomegranate import *
PatientAge = DiscreteDistribution({’0-30’:0.10, ’31-65’:0.30, ’65+’:0.60})
CTScanResult = DiscreteDistribution({’Ischemic Stroke’:0.7, ’Hemmorraghic Stroke’:0.3})
MRIScanResult = DiscreteDistribution({’Ischemic Stroke’:0.7, ’Hemmorraghic Stroke’:0.3})
Anticoagulants = DiscreteDistribution({’Used’:0.5 ,’Not used’:0.5})
StrokeType = ConditionalProbabilityTable(
[[’Ischemic Stroke’,’Ischemic Stroke’,’Ischemic Stroke’,0.8],
[’Ischemic Stroke’,’Hemmorraghic Stroke’,’Ischemic Stroke’,0.5],
[’Hemmorraghic Stroke’,’Ischemic Stroke’,’Ischemic Stroke’,0.5],
[’Hemmorraghic Stroke’,’Hemmorraghic Stroke’,’Ischemic Stroke’,0],
[’Ischemic Stroke’,’Ischemic Stroke’,’Hemmorraghic Stroke’,0],
[’Ischemic Stroke’,’Hemmorraghic Stroke’,’Hemmorraghic Stroke’,0.4],
[’Hemmorraghic Stroke’,’Ischemic Stroke’,’Hemmorraghic Stroke’,0.4],
[’Hemmorraghic Stroke’,’Hemmorraghic Stroke’,’Hemmorraghic Stroke’,0.9],
[’Ischemic Stroke’,’Ischemic Stroke’,’Stroke Mimic’,0.2],
[’Ischemic Stroke’,’Hemmorraghic Stroke’,’Stroke Mimic’,0.1],
[’Hemmorraghic Stroke’,’Ischemic Stroke’,’Stroke Mimic’,0.1],
[’Hemmorraghic Stroke’,’Hemmorraghic Stroke’,’Stroke Mimic’,0.1]],[CTScanResult, ,→ MRIScanResult])
Mortality = ConditionalProbabilityTable(
[[’Ischemic Stroke’,’Used’,’False’,0.28],
[’Hemmorraghic Stroke’,’Used’,’False’,0.99], [’Stroke Mimic’,’Used’,’False’,0.1],
[’Ischemic Stroke’,’Not used’,’False’,0.56],
[’Hemmorraghic Stroke’,’Not used’,’False’,0.58],
[’Stroke Mimic’,’Not used’,’False’,0.05],
[’Ischemic Stroke’,’Used’,’True’,0.72],
[’Hemmorraghic Stroke’,’Used’,’True’,0.01], [’Stroke Mimic’,’Used’,’True’,0.9],
[’Ischemic Stroke’,’Not used’,’True’,0.44],
[’Hemmorraghic Stroke’,’Not used’,’True’,0.42],
[’Stroke Mimic’,’Not used’,’True’,0.95]],[StrokeType, Anticoagulants]) Disability = ConditionalProbabilityTable(
[[’Ischemic Stroke’,’0-30’,’Negligible’,0.80],
[’Hemmorraghic Stroke’,’0-30’,’Negligible’,0.70],
[’Stroke Mimic’,’0-30’,’Negligible’,0.9],
[’Ischemic Stroke’,’31-65’,’Negligible’,0.60],
[’Hemmorraghic Stroke’,’31-65’,’Negligible’,0.50],
[’Stroke Mimic’,’31-65’,’Negligible’,0.4],
[’Ischemic Stroke’,’65+’,’Negligible’,0.30],
[’Hemmorraghic Stroke’,’65+’,’Negligible’,0.20],
[’Stroke Mimic’,’65+’,’Negligible’,0.1],
[’Ischemic Stroke’,’0-30’,’Moderate’,0.1],
[’Hemmorraghic Stroke’,’0-30’,’Moderate’,0.2],
[’Stroke Mimic’,’0-30’,’Moderate’,0.05],
[’Ischemic Stroke’,’31-65’,’Moderate’,0.3],
[’Hemmorraghic Stroke’,’31-65’,’Moderate’,0.4],
[’Stroke Mimic’,’31-65’,’Moderate’,0.3],
[’Ischemic Stroke’,’65+’,’Moderate’,0.4],
[’Hemmorraghic Stroke’,’65+’,’Moderate’,0.2],
[’Stroke Mimic’,’65+’,’Moderate’,0.1],
[’Ischemic Stroke’,’0-30’,’Severe’,0.1],
[’Hemmorraghic Stroke’,’0-30’,’Severe’,0.1],
[’Stroke Mimic’,’0-30’,’Severe’,0.05],
[’Ischemic Stroke’,’31-65’,’Severe’,0.1],
[’Hemmorraghic Stroke’,’31-65’,’Severe’,0.1],
[’Stroke Mimic’,’31-65’,’Severe’,0.3],
[’Ischemic Stroke’,’65+’,’Severe’,0.3],
[’Hemmorraghic Stroke’,’65+’,’Severe’,0.6],
[’Stroke Mimic’,’65+’,’Severe’,0.8]],[StrokeType,PatientAge])
s1 = State(PatientAge, name=”PatientAge”) s2 = State(CTScanResult, name=”CTScanResult”) s3 = State(MRIScanResult, name=”MRIScanResult”) s4 = State(StrokeType, name=”StrokeType”) s5 = State(Anticoagulants, name=”Anticoagulants”) s6 = State(Mortality, name=”Mortality”) s7 = State(Disability, name=”Disability”) model = BayesianNetwork(“Diagnosing”)

model.add_states(s1,s2,s3,s4,s5,s6,s7)
model.add_transition(s2,s4) model.add_transition(s3,s4)
model.add_transition(s4,s6) model.add_transition(s5,s6)
model.add_transition(s1,s7) model.add_transition(s4,s7) model.bake() marginals = model.predict_proba({})
p1 = model.predict_proba({’PatientAge’:’31-65’,’CTScanResult’:’Ischemic Stroke’})[5].
,→ parameters[0][“True”] p2 = model.predict_proba({’PatientAge’:’65+’,’MRIScanResult’:’Hemmorraghic Stroke’})[6].
,→ parameters[0][“Moderate”] p3 = model.predict_proba({’PatientAge’:’65+’,’CTScanResult’:’Hemmorraghic Stroke’,’
,→ MRIScanResult’:’Ischemic Stroke’})[3].parameters[0][“Stroke Mimic”] p4 = model.predict_proba({’PatientAge’:’0-30’})[4].parameters[0][“Not used”] print(p1) print(p2) print(p3) print(p4)