probabilistic graphical models, factorization and parameters [Q]

In a “deep learning and graphical models class” we recently started an intro unit on probabilistic graphical models. The first section is about factoring joint distributions and determining the total number of parameters needed.

For example, here’s an unanswered question from our lecture slides:

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“Let A be a random variable (RV) with support {0, 1, 2}. Similarly, let B, C and D be random variables with supports {0, 1}, {1, 2, 3} and {10, 20}.

  1. Write down the joint distribution of A, B, C and D in a factored form. How many numbers (parameters) are needed to fully specify this joint distribution? Write down all factorizations that are possible for P(A, B, C) and P(A, B).

  2. If we know that P(A|B, C, D) = P(A|B) and P(C|D) = P(C), then what is the number of parameters needed to specify the join distribution P(A, B, C, D)?”

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Can someone point me in the right direction on reading resources (or better yet, explain how one should make sense of these sort of questions)?

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Nevin Manimala

Nevin Manimala is interested in blogging and finding new blogs https://nevinmanimala.com

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