A graph approach to generate all possible regression submodels

Authors:
Cristian Gatu;Petko I. Yanev;Erricos J. Kontoghiorghes
Affiliations:
Institut d'informatique, Université de Neuchítel, Switzerland and Faculty of Computer Science, "Alexandru Ioan Cuza" University of Iasi, Romania;INRIA/IRISA, Rennes, France and Faculty of Mathematics and Informatics, University of Plovdiv "Paisii Hilendarski," Bulgaria;Department of Public and Business Administration, University of Cyprus, Cyprus and School of Computer Science and Information Systems, Birkbeck College, UK
Venue:
Computational Statistics & Data Analysis
Year:
2007

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Abstract

A regression graph to enumerate and evaluate all possible subset regression models is introduced. The graph is a generalization of a regression tree. All the spanning trees of the graph are minimum spanning trees and provide an optimal computational procedure for generating all possible submodels. Each minimum spanning tree has a different structure and characteristics. An adaptation of a branch-and-bound algorithm which computes the best-subset models using the regression graph framework is proposed. Experimental results and comparison with an existing method based on a regression tree are presented and discussed.