# As then we should added the edge instead of 32 first

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as , then we should added the edge instead of ( 3.2 . First, order the variables according to their topological order in G. Without loss of generality, we rename the variables according to their topological order: ,where is the variable to be marginalized. Note that using the above order, running the minimal I-map algorithm will exactly result in G due to the local Markov assumption. Second, add these variables to using the order above, while skipping , and use the independencies that can be read from G about P to select a parent set for each variable. For the variables , adding each of them to G0 results in the same parent set as in G : that is, . Where and is the parent set of variable X in G and respectively. In fact, we can generalize the above relationship for any variable such that . That is, . To see why this is true for , if was not selected as a parent for then , moreover . Since skipping will not change the previous assertions, the parent set of will remain the same in as it still satisfies the local Markov assumption. Therefore, the only variables that will be affected by skipping are those variables that has as a parent in G , i.e., the children on in G . For e ach child of, we n e e d to find a n ew p arent set. Let’s consider on e of thes e children a Must retain its old p arent set in G , other than, since from G , we know that. Therefore, we just need to replace with a set of variables that acts as a surrogate for in parenting . Using the local Markov assumption, blocks some information flow to , therefore these surrogate variables must block the same set of paths while themselves cannot be d-separated from when is not observed. Moreover, these variables must appear in the topological order before. For each parent of in G , , we know that when is not observed due to the active trail .Therefore,. Since all such parents must appear before

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• Spring '13
• Dr.ZAre
• Probability theory, Pearson product-moment correlation coefficient, active trail, G. Therefore, G. Moreover, Soheila Molaei

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