A Comparison of Algorithms for Learning Hidden Variables in Bayesian Factor Graphs in Reduced Normal Form

Bayesian-directed acyclic discrete-variable graphs are reduced to a simplified normal form made up of only replicator units (or equal constraint units), source, and single-input/single-output blocks. In this framework, the same adaptation algorithm can be applied to all the parametric blocks. We obtain and compare adaptation rules derived from a constrained maximum likelihood formulation and a minimum Kullback-Leibler divergence criterion using Karush-Kuhn-Tucker conditions. The learning algorithms are compared with two other updating equations based on localized decisions and on a variational approximation, respectively. The performance of the various algorithms is verified on synthetic data sets for various architectures. Factor graphs in reduced normal form provide an appealing framework for rapid deployment of Bayesian-directed graphs in the applications.