Limited-memory belief propagation via nested optimization

Abstract

In this work we express resource-efficient MAP inference as joint optimization problem w.r.t. (i) messages (i.e. reparametrizations) and (ii) surrogate potentials that are upper bounds for the problem of interest and allow efficient inference. We show that resulting nested optimization task can be solved on trees by a convergent and efficient algorithm, and that its loopy extension also returns convincing MAP solutions in practice. We demonstrate the utility of the method on dense correspondence and image completion problems.