1. From the joint distribution defined by the graphical model, determine if the conditional independence holds:...

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1. From the joint distribution defined by the graphical model, determine if the conditional independence holds: ALL FIE, B, and provide brief explanation (5 points). 2. Given an undirected chain probabilistic-graphical-model of five nodes in the order, x1, x2. X3, X4, X5. please use the sum-product algorithm to derive the marginal p(x3) from x where x = [X1, X2, X3, X4, xs] (7 points). 3. Suppose we are given a set of N observations of the input vector x, which we denote collectively by a data matrix X whose nth row is x with n = 1,..., N. The corresponding target values are given by =(.....x). The likelihood function is defined as p(t|X. w. p) = II p. x. w. B-1). Please draw the directed probabilistic graphical model corresponding to the likelihood function (5 points). 4. Please briefly explain each step of the general EM algorithm (3 points). 1. From the joint distribution defined by the graphical model, determine if the conditional independence holds: ALL FIE, B, and provide brief explanation (5 points). 2. Given an undirected chain probabilistic-graphical-model of five nodes in the order, x1, x2. X3, X4, X5. please use the sum-product algorithm to derive the marginal p(x3) from x where x = [X1, X2, X3, X4, xs] (7 points). 3. Suppose we are given a set of N observations of the input vector x, which we denote collectively by a data matrix X whose nth row is x with n = 1,..., N. The corresponding target values are given by =(.....x). The likelihood function is defined as p(t|X. w. p) = II p. x. w. B-1). Please draw the directed probabilistic graphical model corresponding to the likelihood function (5 points). 4. Please briefly explain each step of the general EM algorithm (3 points).