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Significant progress has been made in developing approximate inference methods, such as the family of belief propagation algorithms, for summation tasks (computing marginal probabilities and partition functions) and MAP estimation (finding optimal configurations).However "mixed" inference tasks that include more than one such variable elimination operator are significantly more difficult. This class of problems include "marginal MAP" problems that predict a subcomponent of the full model, and decision-making problems such as Maximum Expected Utility tasks. We give a general variational framework describing mixed inference problems, in which analogues of the Bethe, tree-reweighted, and mean field approximations can be applied, resulting in new message-passing > approximations on these tasks. Host: Misha Chertkov, chertkov@lanl.gov, 665-8119 |