def exact_bayesian():
'''
bayesian_inference
'''
A = Factor(name='A', values=[0, 1], cpd=[0.5, 0.5])
B = Factor(name='B', values=[0, 1], cpd=[0.5, 0.5])
C = Factor(name='C|A,B',
full='C',
values=[0, 1],
cond=[A, B],
cpd=[1, 0, 1, 0, 1, 0, 0, 1])
print C.query2(query=[A], evidence={C: 0, B: 0})
def bayesian_inference():
'''
bayesian_inference
'''
A = Factor(name='A', values=[0, 1], cpd=[0.6, 0.4])
B = Factor(name='B', values=[0, 1], cpd=[0.7, 0.3])
C = Factor(name='C|A,B',
full='C',
values=[0, 1],
cond=[A, B],
cpd=[0.7, 0.3, 0.9, 0.1, 0.8, 0.2, 0.6, 0.4])
print C.joint().marginal(B.var[-1]).reduce(var=C.var[-1], value=0).norm()
def cancer_example():
'''
Cancer example
'''
C = Factor(name='Cancer', values=["no", "yes"], cpd=[0.999, 0.001])
T = Factor(name='Test',
values=["pos", "neg"],
cond=[C],
cpd=[0.2, 0.8, 0.9, 0.1])
print C
print T
print T.joint()
print T.uncond()
R = T.joint().query2(query=[C], evidence={T: 'pos'})
R.name = "Tested once"
print R
def cancer_example():
'''
Cancer example
'''
C = Factor(name='Cancer', values=["no", "yes"],
cpd=[0.999, 0.001])
T = Factor(name='Test', values=["pos", "neg"],
cond=[C], cpd=[0.2, 0.8, 0.9, 0.1])
## print C
## print T
## print T.joint()
## print T.uncond()
## R = T.query(query=[C], evidence={T:'pos'})
print "First algorithm"
print T._query1(query=[C], evidence=[T])
print "Second algorithm"
print T._query2(query=[C], evidence=[T])
def student_example():
'''
bayesian_inference
'''
D = Factor(name='Difficulty', values=[0, 1], cpd=[0.6, 0.4])
I = Factor(name='Intelligence', values=['low', 'high'], cpd=[0.7, 0.3])
G = Factor(name='Grade|I,D', values=[1, 2, 3],
cond=[D, I], cpd=[0.3, 0.4, 0.3,
0.05, 0.25, 0.7,
0.9, 0.08, 0.02,
0.5, 0.3, 0.2],)
S = Factor(name='SAT|I', values=[0, 1], cond=[I],
cpd=[0.95, 0.05, 0.2, 0.8])
L = Factor(name='Letter|G', values=[0, 1], cond=[G],
cpd=[0.1, 0.9, 0.4, 0.6, 0.99, 0.01])
BN = Bayesian([D, I, S, G, L])
print BN.joint().query(query=[I], evidence={G:3, D:1})
print BN.joint().query(query=[I], evidence=[G, D])
print BN.joint().query(query=[I], evidence=[D])
print BN.joint().query(query=[I], evidence=[G])
def local_inference():
A = Factor(name='A', values=[0, 1], cpd=[0.2, 0.8])
B = Factor(name='B', values=[0, 1], cond=[A], cpd=[0.6, 0.4, 0.3, 0.7])
C = Factor(name='C', values=[0, 1], cond=[B], cpd=[0.6, 0.4, 0.3, 0.7])
D = Factor(name='D', values=[0, 1], cond=[C], cpd=[0.6, 0.4, 0.3, 0.7])
E = Factor(name='E', values=[0, 1], cond=[D], cpd=[0.6, 0.4, 0.3, 0.7])
F = Factor(name='F', values=[0, 1], cond=[E], cpd=[0.6, 0.4, 0.3, 0.7])
G = Factor(name='G', values=[0, 1], cond=[F], cpd=[0.6, 0.4, 0.3, 0.7])
## print A.uncond()
## print B.uncond()
## print C.uncond()
## print D.uncond()
## print E.uncond()
## print F.uncond()
## print B.uncond()
## print B.query(query=[B], evidence=[])
## print (B*A).marginal(var=A.cons)
## print C.uncond()
## print C.query(query=[C], evidence=[])
## print C.query(query=[C], evidence=[B])
## print C
print C._query2(query=[C], evidence=[A, B])
## print C.uncond()
## print (C*B*A).marginal(A.cons).marginal(B.cons)
## print (C*D).marginal(var=D.cons)
## print C.query(query=[C], evidence=[A, B])
A = Factor(name='A', values=[0, 1], cpd=[0.01, 0.99])
B = Factor(name='B', values=[0, 1], cond=[A], cpd=[0.96, 0.04, 0.93, 0.07])
C = Factor(name='C', values=[0, 1], cond=[B], cpd=[0.96, 0.04, 0.93, 0.07])
D = Factor(name='D', values=[0, 1], cond=[C], cpd=[0.96, 0.04, 0.93, 0.07])
E = Factor(name='E', values=[0, 1], cond=[D], cpd=[0.96, 0.04, 0.93, 0.07])
F = Factor(name='F', values=[0, 1], cond=[E], cpd=[0.96, 0.04, 0.93, 0.07])
G = Factor(name='G', values=[0, 1], cond=[F], cpd=[0.96, 0.04, 0.93, 0.07])