Optimized Realization of Bayesian Networks in Reduced Normal Form using Latent Variable Model

Bayesian networks in their Factor Graph Reduced Normal Form (FGrn) are a powerful paradigm for implementing inference graphs. Unfortunately, the computational and memory costs of these networks may be considerable, even for relatively small networks, and this is one of the main reasons why these structures have often been underused in practice. In this work, through a detailed algorithmic and structural analysis, various solutions for cost reduction are proposed. An online version of the classic batch learning algorithm is also analyzed, showing very similar results (in an unsupervised context); which is essential even if multilevel structures are to be built. The solutions proposed, together with the possible online learning algorithm, are included in a C++ library that is quite efficient, especially if compared to the direct use of the well-known sum-product and Maximum Likelihood (ML) algorithms. The results are discussed with particular reference to a Latent Variable Model (LVM) structure.Comment: 20 pages, 8 figure

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