Statistical Parameter Learning for Belief Networks with Fixed Structure

In this report, we address the problem of parameter learning for belief networks with fixed structure based on empirical observations. Both complete and incomplete (data) observations are included. Given complete data, we describe the simple problem of single parameter learning for intuition and then expand to belief networks under appropriate system decomposition. If the observations are incomplete, we first estimate the “missing” observations and treat them as though they are “real” observations, based on which the parameter learning can be executed as in complete data case. We derive a uniform algorithm based on this idea for incomplete data case and present the convergence and optimality properties. Such algorithm is suitable trivially under complete observations. This work was supported by the Center for Satellite and Hybrid Communication Networks, under NASA cooperative agreement NCC3-528.