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Solution to part (c)

Suppose (after observing a value for K) we were to eliminate the variables in order: B, D, A, C, E, G, F, I, H. For each step show which factors are removed and what factor is created. What is the size of the maximum factor created (give both the number of variables and the table size).

Step Eliminate Removed Added
1. B P(B), P(D|A,B) f2(A,D)
2. D P(F|D), f2(A,D) f3(A,F)
3. A P(C|A), P(A), f3(A,F) f4(C,F)
4. C P(E|C), f4(C,F) f5(E,F)
5. E P(H|E,F),f5(E,F) f6(H,F)
6. G P(G), P(I|F,G) f7(I,F)
7. F f6(H,F), f7(I,F) f8(H,I)
8. I P(J|H,I),f1(I), f8(H,I) f9(H,J)
9. H f9(H,J) f10(J)
The largest factor has two variables, and has table size 22=4.
Computational Intelligence online material, ©David Poole, Alan Mackworth and Randy Goebel, 1999

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