Classification and Regression via Integer Optimization. CRIO separates data points in different polyhedral regions. In classification each region is assigned a class, while in regression each region has its own distinct regression coefficients. Computational experimentation with real data sets shows that CRIO is comparable to and often outperforms the current leading methods in classification and regression. The second part describes our cardinality-constrained quadratic mixed-integer optimization algorithm, used to solve subset selection in regression and portfolio selection in asset allocation.

References in zbMATH (referenced in 20 articles )

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  1. Blanco, Victor; Puerto, Justo; Rodriguez-Chia, Antonio M.: On (\ell_p)-support vector machines and multidimensional kernels (2020)
  2. Joki, Kaisa; Bagirov, Adil M.; Karmitsa, Napsu; Mäkelä, Marko M.; Taheri, Sona: Clusterwise support vector linear regression (2020)
  3. Berk, Lauren; Bertsimas, Dimitris: Certifiably optimal sparse principal component analysis (2019)
  4. Corrêa, Ricardo C.; Delle Donne, Diego; Marenco, Javier: On the combinatorics of the 2-class classification problem (2019)
  5. Gopalswamy, Karthick; Fathi, Yahya; Uzsoy, Reha: Valid inequalities for concave piecewise linear regression (2019)
  6. Palagi, Laura: Global optimization issues in deep network regression: an overview (2019)
  7. Blanco, Víctor; Puerto, Justo; Salmerón, Román: Locating hyperplanes to fitting set of points: a general framework (2018)
  8. Liu, Jiapeng; Liao, Xiuwu; Huang, Wei; Yang, Jian-bo: A new decision-making approach for multiple criteria sorting with an imbalanced set of assignment examples (2018)
  9. Benati, Stefano; Puerto, Justo; Rodríguez-Chía, Antonio M.: Clustering data that are graph connected (2017)
  10. Bertsimas, Dimitris; Dunn, Jack: Optimal classification trees (2017)
  11. Verwer, Sicco; Zhang, Yingqian: Learning decision trees with flexible constraints and objectives using integer optimization (2017)
  12. Amaldi, E.; Coniglio, S.; Taccari, L.: Discrete optimization methods to fit piecewise affine models to data points (2016)
  13. Sun, Lei; Nikolaev, Alexander G.: Mutual information based matching for causal inference with observational data (2016)
  14. Brandner, Hubertus; Lessmann, Stefan; Voß, Stefan: A memetic approach to construct transductive discrete support vector machines (2013) ioport
  15. Carrizosa, Emilio; Romero Morales, Dolores: Supervised classification and mathematical optimization (2013)
  16. Toriello, Alejandro; Vielma, Juan Pablo: Fitting piecewise linear continuous functions (2012)
  17. Brooks, J. Paul: Support vector machines with the ramp loss and the hard margin loss (2011)
  18. Sun, Minghe: A mixed integer programming model for multiple-class discriminant analysis (2011)
  19. Nguyen, T. D.; Welsch, R.: Outlier detection and least trimmed squares approximation using semi-definite programming (2010)
  20. Bertsimas, Dimitris; Shioda, Romy: Classification and regression via integer optimization (2007)