cse250ahw3 - CSE 250a Assignment 3 Out Tue Oct 12 Due Tue...

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CSE 250a. Assignment 3 Out: Tue Oct 12 Due: Tue Oct 19 3.1 Node ordering Recall the alarm belief network (BN) described in class, with node ordering { B, E, A, J, M } and directed acyclic graph (DAG) shown below: B J A M E Draw the (minimal) DAGs that would be required to represent this same joint distribution for the following alternative node orderings: (a) { A, J, M, B, E } (b) { A, B, J, E, M } (c) { B, M, J, A, E } (d) { B, A, J, E, M } (e) { J, B, M, A, E } (f) { J, A, B, E, M } It is not necessary to compute the CPTs in each of these alternative BNs. However, for each DAG, you should briefly justify the edges that you include or omit by appealing to properties of conditional indepen- dence. 1
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3.2 Stochastic simulation Consider the belief network shown below, with n binary random variables B i ∈{ 0 , 1 } and an integer random variable Z . Let f ( B ) = n i =1 2 i - 1 B i denote the nonnegative integer whose binary representation is given by B n B n - 1 . . . B 2 B 1 . Suppose that each bit has prior probability P ( B i =1) = 1 2 , and that P ( Z | B 1 , B 2 , . . . , B n ) = 1 - α 1 + α α | Z - f ( B ) | where 0 < α < 1 is a parameter measuring the amount of noise in the conversion from binary to decimal. (Larger values of α indicate greater levels of noise.) bits B i integer Z ...
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  • Spring '10
  • lawrenCe
  • Probability theory, Maximum likelihood, Likelihood function, maximum likelihood estimate, Directed acyclic graph, N-gram

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