The effect of background knowledge ont the most frugal explanations heuristic for the MAP problem

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In Bayesian networks one of the canonical computations is the computation of the most probable explanation (or mode of the joint distribution) over a set of hypothesis variables given evidence in the network. In the most general case, this problem, in the literature known as the MAP problem, is intractable both to compute exactly and to approximate [1, 2, 3]. An alternative to state-of-the-art approximation algorithms like Simulated Annealing and Local Search is the MFE (most frugal explanations) heuristic [1]. This approach uses background knowledge, namely which intermediate variables are relevant and which are irrelevant, in order to lower the amount of variables over which (computationally costly) marginalization is neces- sary. Under certain input constraints MFE can be shown to be tractable. I will research what the e ect of having background knowledge is on the MFE approach to the MAP problem and compare MFE with the state-of-the-art approximation algorithms.
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