Copula selection for graphical models in continuous Estimation of Distribution Algorithms

• Published in: Computational statistics Vol. 29; no. 3-4; pp. 685 - 713
• Main Authors: Salinas-Gutiérrez, Rogelio, Hernández-Aguirre, Arturo, Villa-Diharce, Enrique R.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2014; Springer Nature B.V
• Subjects: Algorithms; Analysis; Economic Theory/Quantitative Economics/Mathematical Methods; Entropy; Gaussian; Genetic algorithms; Learning; Mathematical analysis; Mathematical models; Mathematics and Statistics; Maximum likelihood method; Multivariate analysis; Optimization; Optimization techniques; Original Paper; Polytopes; Population; Probability and Statistics in Computer Science; Probability Theory and Stochastic Processes; Random variables; Statistics; Studies; Multivariate optimization problems; Copula functions; Copula entropies; Likelihood function
• ISSN: 0943-4062; 1613-9658
• DOI: 10.1007/s00180-013-0457-y

This paper presents the use of graphical models and copula functions in Estimation of Distribution Algorithms (EDAs) for solving multivariate optimization problems. It is shown in this work how the incorporation of copula functions and graphical models for modeling the dependencies among variables provides some theoretical advantages over traditional EDAs. By means of copula functions and two well known graphical models, this paper presents a novel approach for defining new EDAs. Either dependence is modeled by a copula function chosen from a predefined set of six functions that aim to cover a wide range of inter-relations. It is also shown how the use of mutual information in the learning of graphical models implies a natural way of employing copula entropies. The experimental results on separable and non-separable functions show that the two new EDAs, which adopt copula functions to model dependencies, perform better than their original version with Gaussian variables.