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

## TL;DR

This paper presents algorithmic and structural solutions to reduce the computational and memory costs of Bayesian networks in reduced normal form, including an efficient online learning algorithm and a C++ library, with a focus on latent variable models.

## Contribution

It introduces cost-reduction techniques and an online learning algorithm for Bayesian networks in FGrn, implemented in a C++ library, enhancing practical usability especially for latent variable models.

## Key findings

- Significant reduction in computational costs.
- Efficient online learning algorithm comparable to batch methods.
- Improved performance in latent variable model structures.

## Abstract

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.