F: 0.2
}),
('Test2', 'Cancer', {
T: 0.9,
F: 0.2
}),
])
"""
Calculations:
∝ * P(Test1, Test2 | Cancer) * P(Cancer)
= ∝ * P(Test1 | Cancer) * P(Test2 | C) * P(Cancer)
= ∝ * 0.9 * 0.9 * 0.01
= 0.17, 0.83
"""
print('P(Cancer | positive results on both tests): ')
print(enumeration_ask('Cancer', dict(Test1=T, Test2=T), cancer).show_approx())
"""
Calculations:
∝ * P(Test1, ¬Test2 | Cancer) * P(Cancer)
= ∝ * P(Test1 | Cancer) * P(¬Test2 | Cancer) * P(Cancer)
= ∝ * 0.9 * 0.2 * 0.01
= 0.00565, 0.99435
"""
print(
'\nP(Cancer | a positive result on test 1, but a negative result on test 2): '
)
print(enumeration_ask('Cancer', dict(Test1=T, Test2=F), cancer).show_approx())
"""
The results do make sense because there is a low chance(0.01) of having cancer
and the probability for each test determining if there is cancer is high (0.9).
('Happy', 'Sunny Raise', {
(T, T): 1.0,
(T, F): 0.7,
(F, T): 0.9,
(F, F): 0.1
})])
#A)
"""
Both Raise and Sunny are both independent, meaning that both do not influence each other
P(Raise | Sunny)
= P(Raise)
= 0.01, 0.99
"""
print('P(Raise | sunny): ')
print(enumeration_ask('Raise', dict(Sunny=T), sunny).show_approx())
"""
∝ * P(Happy | Sunny, Raise) * P(Raise)
= ∝ 1.0 * 0.01
= 0.0142, 0.986
"""
print('\nP(Raise | happy ∧ sunny): ')
print(enumeration_ask('Raise', dict(Happy=T, Sunny=T), sunny).show_approx())
#B)
print('\nP(Raise | happy): ')
print(enumeration_ask('Raise', dict(Happy=T), sunny).show_approx())
print('\nP(Raise | happy ∧ ¬sunny): ')
print(enumeration_ask('Raise', dict(Happy=T, Sunny=F), sunny).show_approx())
"""
(T, T): 0.95,
(T, F): 0.94,
(F, T): 0.29,
(F, F): 0.001
}), ('JohnCalls', 'Alarm', {
T: 0.90,
F: 0.05
}), ('MaryCalls', 'Alarm', {
T: 0.70,
F: 0.01
})])
# Compute P(Alarm | burglary and -earthquake) using the enumeration-ask and elimination-ask algorithms
print("P(Alarm | burglary and -earthquake)")
print(
enumeration_ask('Alarm', dict(Burglary=T, Earthquake=F),
burglary).show_approx())
print(
elimination_ask('Alarm', dict(Burglary=T, Earthquake=F),
burglary).show_approx())
'''
i. This computation solves the probability of alarm going off or not given that there is a burglary and no earthquake
'''
# Compute P(John | burglary and -earthquake) using the enumeration-ask and elimination-ask algorithms
print("\nP(John | burglary and -earthquake)")
print("Enumeration-ask -> " + enumeration_ask(
'JohnCalls', dict(Burglary=T, Earthquake=F), burglary).show_approx())
print("Elimination-ask -> " + elimination_ask(
'JohnCalls', dict(Burglary=T, Earthquake=F), burglary).show_approx())
'''
ii. This computation solves the probability of John calling or not given that there is a burglary and no earthquake.
F: 0.20
}), ('Sprinkler', 'Cloudy', {
T: 0.10,
F: 0.50
}),
('WetGrass', 'Sprinkler Rain', {
(T, T): 0.99,
(T, F): 0.90,
(F, T): 0.90,
(F, F): 0.00
})])
# Compute P(Cloudy)
print('P(Cloudy)')
print("Enumeration-ask -> " +
enumeration_ask('Cloudy', dict(), weatherA).show_approx())
# Compute P(Sprinkler | cloudy)
print('\nP(Sprinkler | cloudy)')
print("Enumeration-ask -> " +
enumeration_ask('Sprinkler', dict(Cloudy=T), weatherA).show_approx())
# Compute P(Cloudy| the sprinkler is running and it’s not raining)
print('\nP (Cloudy | sprinker and -rain')
print("Enumeration-ask -> " + enumeration_ask(
'Cloudy', dict(Sprinkler=T, Rain=F), weatherA).show_approx())
# Compute P(WetGrass | it’s cloudy, the sprinkler is running and it’s raining)
print('\nP (WetGrass | cloudy and sprinkler and rain')
print("Enumeration-ask -> " + enumeration_ask(
'WetGrass', dict(Cloudy=T, Sprinkler=T, Rain=T), weatherA).show_approx())
('Sprinkler', 'Cloudy', {
T: 0.1,
F: 0.5
}), ('Rain', 'Cloudy', {
T: 0.8,
F: 0.2
}),
('WetGrass', 'Sprinkler Rain', {
(T, T): 0.99,
(T, F): 0.90,
(F, T): 0.90,
(F, F): 0.00
})])
# i
print("i.", enumeration_ask('Cloudy', dict(), bayes_net).show_approx())
# ii
print("ii.",
enumeration_ask('Sprinkler', dict(Cloudy=T), bayes_net).show_approx())
# iii
print(
"iii.",
enumeration_ask('Cloudy', dict(Sprinkler=T, Rain=T),
bayes_net).show_approx())
# iv
print(
"iv.",
enumeration_ask('WetGrass', dict(Cloudy=T, Sprinkler=T, Rain=T),
bayes_net).show_approx())
# v
print("v.",
from tools.aima.probability import BayesNet, enumeration_ask
# Utility variables
T, F = True, False
# create the Bayes Network
happy = BayesNet([
('Sunny', '', 0.7),
('Raise', '', 0.01),
('Happy', 'Sunny Raise', {(T, T): 1.0, (T, F): 0.7, (F, T): 0.9, (F, F): 0.1})
])
print("Exercise 5.3")
# a.i. P(Raise | sunny)
print("a. i. ", enumeration_ask('Raise', dict(Sunny=T), happy).show_approx())
# a.ii. P(Raise | happy ^ sunny)
print(" ii. ", enumeration_ask('Raise', dict(Happy=T, Sunny=T), happy).show_approx())
# b.i. P(Raise | happy)
print("b. i. ", enumeration_ask('Raise', dict(Happy=T), happy).show_approx())
# b.ii. P(Raise | happy ^ -sunny)
print(" ii. ", enumeration_ask('Raise', dict(Happy=T, Sunny=F), happy).show_approx())
"""
The results don't makes sense to me; this is the case for diagnostic statistics.
"""
# Utility variables
T, F = True, False
# From AIMA code (probability.py) - tow-cause happiness example
happiness = BayesNet([('Sunny', '', 0.7), ('Raise', '', 0.01),
('Happy', 'Sunny Raise', {
(T, T): 1.0,
(T, F): 0.7,
(F, T): 0.9,
(F, F): 0.1
})])
# a. i) Compute P(Raise | sunny) using the enumeration-ask and elimination-ask algorithms
print("P(Raise | sunny)")
print("Enumeration-ask -> " +
enumeration_ask('Raise', dict(Sunny=T), happiness).show_approx())
print("Elimination-ask -> " +
elimination_ask('Raise', dict(Sunny=T), happiness).show_approx())
# a. ii) Compute P(Raise | happy and sunny) using the enumeration-ask and elimination-ask algorithms
print("\nP(Raise | happy and sunny)")
print(
"Enumeration-ask -> " +
enumeration_ask('Raise', dict(Happy=T, Sunny=T), happiness).show_approx())
print(
"Elimination-ask -> " +
elimination_ask('Raise', dict(Happy=T, Sunny=T), happiness).show_approx())
'''
Hand-work
a. i) P(Raise | sunny)
= <P(raise | sunny), P(-raise | sunny)>
}), ('Rain', 'Cloudy', {
T: 0.8,
F: 0.2
}),
('WetGrass', 'Sprinkler Rain', {
(T, T): 0.99,
(T, F): 0.9,
(F, T): 0.9,
(F, F): 0.0
})])
'''
i. P(Cloudy) = 0.5
= 0.5, 0.5
'''
print(enumeration_ask('Cloudy', dict(), climate).show_approx())
'''
ii.P(Sprinker | cloudy) = 0.1
= 0.1, 0.9
'''
print(enumeration_ask('Sprinkler', dict(Cloudy=T), climate).show_approx())
'''
iii. P(Cloudy| the sprinkler is running and it’s not raining)
= ∝ * P(Sprinkler, ¬Rain | Cloudy * P(Cloudy)
= ∝ * 0.1 * 0.2 * 0.5
= ∝ * 0.01, 0.2
= 0.0476, 0.952
'''
print(
enumeration_ask('Cloudy', dict(Sprinkler=T, Rain=F),
climate).show_approx())