Normal Factor Graphs as Probabilistic Models

TL;DR

This paper introduces normal factor graphs (NFGs) as a versatile probabilistic modeling framework that unifies various existing models and explores their dualities, transformations, and inference algorithms.

Contribution

It presents NFGs as a new framework unifying existing models, highlighting their duality, transformations, and inference methods.

Findings

NFGs unify factor graphs, convolutional factor graphs, and cumulative distribution networks.

NFG models exhibit a duality between constrained and generative forms.

Algorithms for computing NFG exterior functions and inference are discussed.

Abstract

We present a new probabilistic modelling framework based on the recent notion of normal factor graph (NFG). We show that the proposed NFG models and their transformations unify some existing models such as factor graphs, convolutional factor graphs, and cumulative distribution networks. The two subclasses of the NFG models, namely the constrained and generative models, exhibit a duality in their dependence structure. Transformation of NFG models further extends the power of this modelling framework. We point out the well-known NFG representations of parity and generator realizations of a linear code as generative and constrained models, and comment on a more prevailing duality in this context. Finally, we address the algorithmic aspect of computing the exterior function of NFGs and the inference problem on NFGs.