Discussion
Consider the following statements about Bayesian networks.
1. The graph asserts conditional independences between the variables
2. Each node carries a distribution given each combination of parent values
3. Exact inference is polynomial in every network
Which of the statements given above is or are correct?
Answer: B
The first two are correct. Exact inference is NP hard in general, and its cost depends on the network's structure through the size of the largest intermediate factor. Tree structured networks are polynomial, which is why structure matters so much. Assuming that a compact representation implies cheap inference is a natural but mistaken step, and the two properties must be established separately.
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