A mean field approach to MAP in belief networks

The maximum a posteriori probability (MAP) problem is to find the most probable instantiation of all uninstantiated variables, given an instantiation of a set of variables in a Bayesian belief network (BBN). MAP is known to be NP-hard. To circumvent the high computational complexity, we propose a neural network approach based on the mean field theory to approximate the MAP problem. In this approach, a given BBN is treated as a neural network with an energy function defined in such a way that the MAP solution corresponds to the global minimum energy state. The mean field equation is then derived. We also propose a method called resettling to further improve the solution accuracy. A series of computer experiment shows that this approach may lead to effective and accurate solutions to MAP problems