UCL

COMP 80

1. Independence in Graphical Models (a) Suppose that X; and X5 are two independent random variables, where each can take one of three states. Here is a probability table P describing their joint distribution, P;; = p(X1 = i, X2 = j): 7 042 0.12 P=1{001 7?7 0.02 0.03 0.21 7 Some entries are missing. Is it possible to deduce them? If yes, do so, if not explain why. [5 marks] (b) Consider the following Markov Network on the variables X;: Write down the set of all the conditional and marginal independence statements that are true for the marginal distribution P(X3, X4, Xe). [5 marks] (c) Consider the following two graphical models: