Variational Algorithms for Marginal MAP

Qiang Liu; Alexander T. Ihler

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arXiv · 1202.3742

Variational Algorithms for Marginal MAP

Qiang Liu·Alexander T. Ihler

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Abstract

Marginal MAP problems are notoriously difficult tasks for graphical models. We derive a general variational framework for solving marginal MAP problems, in which we apply analogues of the Bethe, tree-reweighted, and mean field approximations. We then derive a "mixed" message passing algorithm and a convergent alternative using CCCP to solve the BP-type approximations. Theoretically, we give conditions under which the decoded solution is a global or local optimum, and obtain novel upper bounds on solutions. Experimentally we demonstrate that our algorithms outperform related approaches. We also show that EM and variational EM comprise a special case of our framework.

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Qiang Liu, Alexander T. Ihler. 2012-02-14. Variational Algorithms for Marginal MAP. https://arxiv.org/abs/1202.3742

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