Bayesian multinets for ViSCoS data
Model construction
Let’s consider Prog.1 data. We divide the data set into two parts, part1= those who have P(F R1 = 1) and part2= those having P(F R1 = 0). We define the model structure for both data sets, such that F Ris the root node in both networks but other variables A, B, C can be either root or leaf nodes and the edges can be different. This structure can be learnt e.g. by camml tool or defined yourself according to dependency analysis. Let’s call the resulting local models as network1 and network2. Two (imaginary) examples are presented in figure.
FR=1 FR=0
A B C
B C
A
Then we learn the model parameters. The prior probabilities P(F R = 1) and P(F R= 0) are learnt from the whole data set. All the other parameters are learnt only from part of data, from part1 for network1 and from part2 for network 2.
Predicting F R
Let’s suppose that A and B points are known for some student. Now we want to update probability to pass the course given this evidence by Bayes rule. Thus, we want to compute P(F R = 1|A = a, B = b), where a, b ∈ {0,1} are known.
We remeber that P(F R = 1|A = a, B = b) = P(F R=1,A=a,B=b)
P(A=a,B=b) . P(F R = 1, A = a, B =b) is calculated only from network1, because it is never true in network2. It is P(F R = 1)P(A = a|F R = 1)P(B = b|A = a). For P(A = a, B = b) we need both networks, because P(A = a, B =b) = P(F R = 1, A = a, B = b) +P(F R = 0, A =a, B = b). Thus, we obtain P(A = a, B =b) = P(F R = 1)P(A = a|F R = 1)P(B =b|A=a) +P(F R= 0)P(A=a|F R= 0)P(B =b|F R = 0).
Now P(F R = 0|A = a, B = b) should be simply 1−P(F R = 1|A = a, B = b) and thus it is the same, which one you compute.
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