Using Expectation Maximization to Find Likely Assignments for Solving CSP's

We present a new probabilistic framework for finding likely variable assignments in difficult constraint satisfaction problems. Finding such assignments is key to efficient search, but practical efforts have largely been limited to random guessing and heuristically designed weighting systems. In contrast, we derive a new version of Belief Propagation (BP) using the method of Expectation Maximization (EM). This allows us to differentiate between variables that are strongly biased toward particular values and those that are largely extraneous. Using EM also eliminates the threat of non-convergence associated with regular BP. Theoretically, the derivation exhibits appealing primal/dual semantics. Empirically, it produces an “EMBP”-based heuristic for solving constraint satisfaction problems, as illustrated with respect to the Quasigroup with Holes domain. EMBP outperforms existing techniques for guiding variable and value ordering during backtracking search on this problem.