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Classification and Regression via Integer Optimization

Sloan School of Management and Operations Research Center, Massachusetts Institute of Technology, E53-363, Cambridge, Massachusetts 02139
Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
dbertsim{at}mit.edu
rshioda{at}uwaterloo.ca

Motivated by the significant advances in integer optimization in the past decade, we introduce mixed-integer optimization methods to the classical statistical problems of classification and regression and construct a software package called CRIO (classification and regression via integer optimization). CRIO separates data points into different polyhedral regions. In classification each region is assigned a class, while in regression each region has its own distinct regression coefficients. Computational experimentations with generated and real data sets show that CRIO is comparable to and often outperforms the current leading methods in classification and regression. We hope that these results illustrate the potential for significant impact of integer optimization methods on computational statistics and data mining.

Subject classifications: programming; integer; applications; statistics; nonparametric.
History: Received November 2002; revision received April 2006; accepted April 2006.