Factor Graph Grammars

TL;DR

This paper introduces factor graph grammars (FGGs), a novel formalism using hyperedge replacement graph grammars that can generate and perform inference on a broader class of models than existing graphical model representations.

Contribution

It proposes FGGs as a new framework for representing and performing inference on complex graphical models, extending beyond traditional methods like plate notation and sum-product networks.

Findings

FGGs can describe more general models than existing notations.

Inference on FGGs can be performed without enumerating all generated graphs.

Exact and tractable inference is possible for many cases using a generalized variable elimination.

Abstract

We propose the use of hyperedge replacement graph grammars for factor graphs, or factor graph grammars (FGGs) for short. FGGs generate sets of factor graphs and can describe a more general class of models than plate notation, dynamic graphical models, case-factor diagrams, and sum-product networks can. Moreover, inference can be done on FGGs without enumerating all the generated factor graphs. For finite variable domains (but possibly infinite sets of graphs), a generalization of variable elimination to FGGs allows exact and tractable inference in many situations. For finite sets of graphs (but possibly infinite variable domains), a FGG can be converted to a single factor graph amenable to standard inference techniques.