CPD computations for Bayesian network

student_reasoning.py

#I'm taking the STanford on line course Probabilistic Graphical Models <pgm-class.org>
# They have a simple  example of a Bayesian network for a Student letter of reference
# the code below was originally posted by a fellow classmate taking the class
# it really helped me in understanding how to do computations on conditional probability tables (CPDs) that 
# form the heart of Bayesian networks

from numpy import *
P_I = array([
[0.7,0.3]
])
print "Probability of Intelligence: P(I)"
print P_I
P_D = array([
[0.6,0.4]
])
print "Probability of Intelligence: P(D)"
print P_D

print "Join Probability of Intelligence and Difficulty: P(I,D)"
P_ID = P_I.T.dot(P_D)
print P_ID
print "... flattened and copied out for easy multiplication with P(G|I,D)"
P_ID = array([P_ID.ravel()]).T
P_ID = hstack([P_ID,P_ID,P_ID])
print P_ID

print "Conditional probability of grade P(G|I,D)"
P_G_ID = array([
	[0.3,0.4,0.3],
	[0.05,0.25,0.7],
	[0.9,0.08,0.02],
	[0.5,0.3,0.2],
])
print P_G_ID

print "Joint probability of grade, intelligence and difficulty P(G,I,D) = P(G|I,D)*P(I)*P(D) = P(G|I,D)*P(I,D)"
P_GID = P_G_ID * P_ID 
P_GID = P_GID 
print P_GID

print "Joint probability of grade and difficulty with intelligence = i0 P(G,I=i0,D) = P(G|I=i0,D)*P(D) = P(G|I=i0,D)*P(D)"
P_Dstack = hstack([P_D.T,P_D.T,P_D.T])
P_Gi0D = P_G_ID[0:2,:] * P_Dstack
print P_Gi0D

print "Joint probability of grade and difficulty with intelligence = i1 P(G,I=i1,D) = P(G|I=i1,D)*P(D)"
P_Dstack = hstack([P_D.T,P_D.T,P_D.T])
P_Gi1D = P_G_ID[2:,:] * P_Dstack
print P_Gi1D

P_Istack = hstack([P_I.T,P_I.T])
P_S_I = array([
	[0.95,0.05],
	[0.2,0.8],
])
P_SI = P_S_I * P_Istack

P_L_G = array([
	[0.1,0.9],
	[0.4,0.6],
	[0.99,0.01],
])
l1 = 0.9 * P_GID[:,0].sum() + 0.6 * P_GID[:,1].sum() + 0.01 * P_GID[:,2].sum()
l1_i0 = array(P_Gi0D.sum(axis=0)).dot(P_L_G[:,1])
l1_i0_d0 = array(P_G_ID[0,:]).dot(P_L_G[:,1])
l1_i1 = array(P_Gi1D.sum(axis=0)).dot(P_L_G[:,1])
print "Probability of l1\n... (i.e. P(L = l1,G,I,D) = P(L = l1 | G) * P(G|I,D) * P(S|I) * P(I) * P(D) ):", l1
print "Probability of l1 and i0\n... (i.e. P(L = l1,G,I = i0,D) = P(L = l1,| G,I = i0, D) * P(G|I = i0,D) * P(I = i0) * P(D) ):", l1_i0
print "Probability of l1 and i1\n... (i.e. P(L = l1,G,I = i1,D) = P(L = l1,| G,I = i1, D) * P(G|I = i1,D) * P(I = i0) * P(D) ):", l1_i1
print "Probability of l1 and i0 and d0\n... (i.e. P(L = l1,G,I = i0,D = d0) = P(L = l1,| G,I = i0, D = d0) * P(G|I = i0,D = d0) ):", l1_i0_d0