ps3-08 - CS228 Problem Set #3 1 CS 228, Winter 2008 Problem...

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Unformatted text preview: CS228 Problem Set #3 1 CS 228, Winter 2008 Problem Set #3 We have provided approximate lengths with each of the problems to give you a rough estimate of how long we think each answer might be not including diagrams. These are meant to be guidelines only to make sure that answers are concise and readable (for diagrams, the larger the better). 1. Entanglement in DBNs [20 points] (a) [6 points] Prove Proposition 15.2.4: Let I be the influence graph for a 2-TBN B . Then I contains a directed path from X to Y if and only if, in the unrolled DBN, for every t , there exists a directed path from X ( t ) to Y ( t ) for some t t . (b) [10 points] Prove the entanglement theorem, Theorem 15.2.5: Let hG , G i be a fully persistent DBN structure over X = X O , where the state variables X ( t ) are hidden in every time slice, and the observation variables O ( t ) are observed in every time slice. Furthermore, assume that, in the influence graph for G : there is a trail (not necessarily a directed path) between every pair of nodes, i.e., the graph is connected; every state variable X has some directed path to some evidence variable in O ....
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ps3-08 - CS228 Problem Set #3 1 CS 228, Winter 2008 Problem...

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