Factor Graph Grammars
This provides a more general modeling framework than existing notations for researchers in probabilistic graphical models, though it appears incremental as an extension of graph grammars to factor graphs.
The authors tackled the problem of modeling complex probabilistic structures by introducing factor graph grammars (FGGs), which generate sets of factor graphs and enable exact and tractable inference without enumerating all graphs, applicable to finite variable domains or finite sets of graphs.
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.