4. [30 pts] Consider a domain with three binary nodes: A, B, and C and the data

Question

4. [30 pts] Consider a domain with three binary nodes: A, B, and C and the data set with three sampled tuples: 0, 1, 1 0, 1, 1 1, 0, 0 (a) [5 pts] How many possible Bayes network structures are there over three nodes? Hint: consider how many ways can the arrows be placed so that the graph is NOT a Bayes network. In the following sub-questions, if the day of your birthday is 0 mod 3, then do structures S1 and S2. If it's 1 mod 3, then do structures S3 and S4. And if it's 2 mod 3, then do structures S5 and S6. S3 CA OB)-- CD

Explanation / Answer

Answer-a

There are 25 possible networks structures: 1 with no arcs, 6 with one arc, 12 with two arcs, and 6 with three arcs.

Answer-b

Number of parameters in each network: 3, 7, 5, 6, 5, 5.

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