Hypergraph Grammars for Knowledge Based Model Construction

Russell G. Almond
Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics, PMLR R0:15-22, 1995.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR0-almond95a, title = {Hypergraph Grammars for Knowledge Based Model Construction}, author = {Almond, Russell G.}, booktitle = {Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics}, pages = {15--22}, year = {1995}, editor = {Fisher, Doug and Lenz, Hans-Joachim}, volume = {R0}, series = {Proceedings of Machine Learning Research}, month = {04--07 Jan}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/r0/almond95a/almond95a.pdf}, url = {https://proceedings.mlr.press/r0/almond95a.html}, abstract = {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.}, note = {Reissued by PMLR on 01 May 2022.} }
Endnote
%0 Conference Paper %T Hypergraph Grammars for Knowledge Based Model Construction %A Russell G. Almond %B Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 1995 %E Doug Fisher %E Hans-Joachim Lenz %F pmlr-vR0-almond95a %I PMLR %P 15--22 %U https://proceedings.mlr.press/r0/almond95a.html %V R0 %X 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. %Z Reissued by PMLR on 01 May 2022.
APA
Almond, R.G.. (1995). Hypergraph Grammars for Knowledge Based Model Construction. Pre-proceedings of the Fifth International Workshop on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research R0:15-22 Available from https://proceedings.mlr.press/r0/almond95a.html. Reissued by PMLR on 01 May 2022.

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