Hypergraph Grammars for Knowledge Based Model Construction
Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics, PMLR R0:15-22, 1995.
Graphical belief networks, including Bayes nets and influence diagrams, can be represented with directed hypergraphs. Each directed hyperedge corresponds to a factor of the joint distribution of all variables in the model. A hyperedge replacement grammar is a collection of rules for replacing hyperedges with hypergraphs. A hyperedge replacement grammar for graphical belief networks defines a collection of graphical belief models. Hyperedge replacement grammars have several interesting implications in the construction of graphical models. (1) They provide a way to represent the process of constructing a graphical model. (2) Coupled with an object-oriented variable type system, provide a convenient method for searching through candidate factors to fill a particular slot in the model graph. (3) They provide a method for integrating high-level and detailed views of a graphical model. (4) They provide a mechanism for representing uncertainty about the model structure.