('Alarm', 'Burglary Earthquake', {(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(Burglary | John and Mary both call).
print(enumeration_ask('Burglary', dict(JohnCalls=T, MaryCalls=T), burglary).show_approx())
# elimination_ask() is a dynamic programming version of enumeration_ask().
print(elimination_ask('Burglary', dict(JohnCalls=T, MaryCalls=T), burglary).show_approx())
# gibbs_ask() is an approximation algorithm helps Bayesian Networks scale up.
print(gibbs_ask('Burglary', dict(JohnCalls=T, MaryCalls=T), burglary).show_approx())
# See the explanation of the algorithms in AIMA Section 14.4.
# rejection_sampling() and likelihood_weighting() are also approximation algorithms.
print(rejection_sampling('Burglary', dict(JohnCalls=T, MaryCalls=T), burglary).show_approx())
print(likelihood_weighting('Burglary', dict(JohnCalls=T, MaryCalls=T), burglary).show_approx())
# P(Alarm | burglary ∧ ¬earthquake)
print('5.1 i: \t' + enumeration_ask('Alarm', dict(Burglary=T, Earthquake=F), burglary).show_approx())
# P(John | burglary ∧ ¬earthquake)
print('5.1 ii: \t' + enumeration_ask('John', dict(Burglary=T, Earthquake=F), burglary).show_approx())
# P(Burglary | alarm)
print('5.1 iii:\t' + enumeration_ask('Burglary', dict(Alarm=T), burglary).show_approx())
'''
Answers to section 5.4 of lab05, for CS 344:
The approximation algorithms give answers that one would expect given their name. They're approximately the right
answer, but not exactly. These algorithms also don't return the same answer every time, but bounce around in
proximity to the true answer. This is because these algorithms work using random sampling. Every time they're run,
they will be computing from a different random sample, which changes the answer. This is also why the answer isn't
exactly the same as the true answer. These algorithms are doing things to decrease the problem space in different
The probability that you have cancer given that you obtained a positive result on both tests.
'''
# Compute P(Cancer | positive results on both tests)
print("\nP(Cancer | positive results on both tests)")
print(enumeration_ask('Cancer', dict(Test1=T, Test2=T), cancer).show_approx())
# elimination_ask() is a dynamic programming version of enumeration_ask().
print(elimination_ask('Cancer', dict(Test1=T, Test2=T), cancer).show_approx())
# gibbs_ask() is an approximation algorithm helps Bayesian Networks scale up.
print(gibbs_ask('Cancer', dict(Test1=T, Test2=T), cancer).show_approx())
# See the explanation of the algorithms in AIMA Section 14.4.
print(
rejection_sampling('Cancer', dict(Test1=T, Test2=T), cancer).show_approx())
print(
likelihood_weighting('Cancer', dict(Test1=T, Test2=T),
cancer).show_approx())
'''
Diagnostic inference. Refer to screen capture and/or turned in paper copy for mathematical explanation.
The probability that you have cancer given that you obtained a positive result on one test and a negative result
on the other test.
'''
# Compute P(Cancer | a positive result on test 1, but a negative result on test 2)
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())
# elimination_ask() is a dynamic programming version of enumeration_ask().
print(elimination_ask('Cancer', dict(Test1=T, Test2=F), cancer).show_approx())
# gibbs_ask() is an approximation algorithm helps Bayesian Networks scale up.
print(enumeration_ask('JohnCalls', dict(Burglary=T, Earthquake=F), burglary).show_approx())
# iii) *P*(Burglary | alarm)
print(enumeration_ask('Burglary', dict(Alarm=T), burglary).show_approx())
# iv) *P*(Burglary | john ∧ mary)
print(enumeration_ask('Burglary', dict(JohnCalls=T, MaryCalls=T), burglary).show_approx())
# These numbers make sense based on the network.
# 5.4
# None of the approximation algorithms match the exact inference algorithms.
# Enum ask (exact inference) is always <0.284, 0.716> but the other algorithms vary in result when you run them.
# The reason why the approximate algorithms change on each run is due to their random nature.
print("Enumeration Ask: ", enumeration_ask('Burglary', dict(JohnCalls=T, MaryCalls=T), burglary).show_approx())
# Rejection sampling is different from exact inference because it generates random samples from the distribution and
# then rejects samples that don't match the evidence. It ends up rejecting many samples, especially when the
# amount of evidence variables are large.
print("Rejection Sampling: ", rejection_sampling('Burglary', dict(JohnCalls=T, MaryCalls=T), burglary, 10000).show_approx())
# Likelihood weighting fixes evidence variables and only varies nonevidence variables in the samples. This makes it
# similar to rejection sampling but it will only produce samples that are consistent with the evidence. It varies from
# exact inference because it is estimating samples when exact does not estimate.
print("Likelihood Weighting: ", likelihood_weighting('Burglary', dict(JohnCalls=T, MaryCalls=T), burglary, 10000).show_approx())
# Gibbs ask does not match with exact inference because it generates random samples. Gibbs ask is a type of MCMC
# that starts at a random state, and then flips a random variable while keeping the evidence variables fixed.
print("Gibbs Ask: ", gibbs_ask('Burglary', dict(JohnCalls=T, MaryCalls=T), burglary).show_approx())
'''
Inference. Refer to screen capture and/or turned in paper copy for mathematical explanation.
The probability that you obtain a raise given that it is sunny.
'''
# Compute P(Raise | sunny)
print("\nP(Raise | sunny)")
print(enumeration_ask('Raise', dict(Sunny=T), happiness).show_approx())
# elimination_ask() is a dynamic programming version of enumeration_ask().
print(elimination_ask('Raise', dict(Sunny=T), happiness).show_approx())
# gibbs_ask() is an approximation algorithm helps Bayesian Networks scale up.
print(gibbs_ask('Raise', dict(Sunny=T), happiness).show_approx())
# See the explanation of the algorithms in AIMA Section 14.4.
print(rejection_sampling('Raise', dict(Sunny=T), happiness).show_approx())
print(likelihood_weighting('Raise', dict(Sunny=T), happiness).show_approx())
'''
Diagnostic inference. Refer to screen capture and/or turned in paper copy for mathematical explanation.
The probability that you obtain a raise given that you are happy and it is sunny.
'''
# Compute P(Raise | happy ∧ sunny)
print("\nP(Raise | happy ∧ sunny)")
print(enumeration_ask('Raise', dict(Happy=T, Sunny=T), happiness).show_approx())
# elimination_ask() is a dynamic programming version of enumeration_ask().
print(elimination_ask('Raise', dict(Happy=T, Sunny=T), happiness).show_approx())
# gibbs_ask() is an approximation algorithm helps Bayesian Networks scale up.
print(gibbs_ask('Raise', dict(Happy=T, Sunny=T), happiness).show_approx())
# See the explanation of the algorithms in AIMA Section 14.4.
(T, T): 0.99,
(T, F): 0.90,
(F, T): 0.90,
(F, F): 0.00
})])
# Compute P(Cloudy)
print("\nP(Cloudy)")
print(enumeration_ask('Cloudy', dict(), cloudy).show_approx())
# elimination_ask() is a dynamic programming version of enumeration_ask().
print(elimination_ask('Cloudy', dict(), cloudy).show_approx())
# gibbs_ask() is an approximation algorithm helps Bayesian Networks scale up.
print(gibbs_ask('Cloudy', dict(), cloudy).show_approx())
# See the explanation of the algorithms in AIMA Section 14.4.
print(rejection_sampling('Cloudy', dict(), cloudy).show_approx())
print(likelihood_weighting('Cloudy', dict(), cloudy).show_approx())
###################################################################################################
# Compute P(Sprinkler | cloudy)
print("\nP(Sprinkler | cloudy)")
print(enumeration_ask('Sprinkler', dict(Cloudy=T), cloudy).show_approx())
# elimination_ask() is a dynamic programming version of enumeration_ask().
print(elimination_ask('Sprinkler', dict(Cloudy=T), cloudy).show_approx())
# gibbs_ask() is an approximation algorithm helps Bayesian Networks scale up.
print(gibbs_ask('Sprinkler', dict(Cloudy=T), cloudy).show_approx())
# See the explanation of the algorithms in AIMA Section 14.4.
print(rejection_sampling('Sprinkler', dict(Cloudy=T), cloudy).show_approx())
print(likelihood_weighting('Sprinkler', dict(Cloudy=T), cloudy).show_approx())
###################################################################################################
Diagnostic inference. Refer to screen capture and/or turned in paper copy for mathematical explanation.
The probability that a burglary occurs given that john and mary both call, which depends on alarm and earthquake as
evidence variables.
'''
# Compute P(Burglary | John and Mary both call).
print("\nP(Burglary | John and Mary both call)")
print(enumeration_ask('Burglary', dict(JohnCalls=T, MaryCalls=T), burglary).show_approx())
# elimination_ask() is a dynamic programming version of enumeration_ask().
print(elimination_ask('Burglary', dict(JohnCalls=T, MaryCalls=T), burglary).show_approx())
# gibbs_ask() is an approximation algorithm helps Bayesian Networks scale up.
print(gibbs_ask('Burglary', dict(JohnCalls=T, MaryCalls=T), burglary).show_approx())
# See the explanation of the algorithms in AIMA Section 14.4.
print(rejection_sampling('Burglary', dict(JohnCalls=T, MaryCalls=T), burglary).show_approx())
print(likelihood_weighting('Burglary', dict(JohnCalls=T, MaryCalls=T), burglary).show_approx())
'''
Causal inference. Refer to screen capture and/or turned in paper copy for mathematical explanation.
The probability that the alarm goes off given that a burglary occurs and there is no earthquake.
'''
# Compute P(Alarm | burglary ∧ ¬earthquake)
print("\nP(Alarm | burglary ∧ ¬earthquake")
print(enumeration_ask('Alarm', dict(Burglary=T, Earthquake=F), burglary).show_approx())
# elimination_ask() is a dynamic programming version of enumeration_ask().
print(elimination_ask('Alarm', dict(Burglary=T, Earthquake=F), burglary).show_approx())
# gibbs_ask() is an approximation algorithm helps Bayesian Networks scale up.
print(gibbs_ask('Alarm', dict(Burglary=T, Earthquake=F), burglary).show_approx())
# See the explanation of the algorithms in AIMA Section 14.4.