Algorithms for the Nearest Assignment Problem.

We consider the following nearest assignment problem (NAP): given a Bayesian network B and probability value q, find a configuration omega of variables in B such that the difference between q and probability of omega is minimized NAP is much harder than conventional inference problems such as finding the most probable explanation in that it is NP-hard even on independent Bayesian networks (IBNs), which are networks having no edges. We propose a two-way number partitioning encoding of NAP on IBNs and then leverage poly-time approximation algorithms from the number partitioning literature to develop algorithms with guarantees for solving NAP. We extend our basic algorithm from IBNs to arbitrary probabilistic graphical models by leveraging cutset-based conditioning, local search and (Rao-Blackwellised) sampling algorithms. We derive approximation and complexity guarantees for our new algorithms and show experimentally that they are quite accurate in practice.