Classification and regression via integer optimization

Operations Research

Volumn 55, Issue 2, 2007, Pages 252-271

  Bertsimas, Dimitris ^a   Shioda, Romy ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Applications; Programming: integer; Statistics: nonparametric

Indexed keywords

COMPUTATIONAL EXPERIMENTATIONS; INTEGER OPTIMIZATION; POLYHEDRAL REGIONS; STATISTICAL PROBLEMS;

CLASSIFICATION (OF INFORMATION); COMPUTATIONAL METHODS; INTEGER PROGRAMMING; PROBLEM SOLVING; REGRESSION ANALYSIS;

OPTIMIZATION;

EID: 34247479715     PISSN: 0030364X     EISSN: 15265463     Source Type: Journal    
DOI: 10.1287/opre.1060.0360     Document Type: Article

References (23)

1. Arthanari, T. S., Y. Dodge. 1993. Mathematical. Progmmming in Statistics. Wiley Classics Library Edition, Wiley-Interscience, New York.
2. Bennett, K. P., J. A. Blue. 1984. Optimal decision trees. R.P.I. Math Report 214, Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY.
3. Bertsimas, D., R. Shioda. 2004. An algorithm for cardinality constraint quadratic optimization. In review.
4. Bienstock, D. 1996. Computational study of families of mixed-integer quadratic programming problems. Math. Programming 74 121-140.
5. Bousquet, O., A. Elisseeff. 2002. Stability and generalization. J. Machine Learn. Res. 2 445-498.
6. Breiman, L., J. Friedman, R. Olshen, C. Stone. 1984. Classification and Regression Trees. Wadsworth International, Belmont, CA.
7. Friedman, J. 1991. Multivariate adaptive regression splines. Ann. Statist. 19(1) 1-67.
8. Friedman, J. H. 1999a. Stochastic gradient boosting. http://www-stat. stanford.edu/~jhf/ftp/stobst.ps.
9. Friedman, J. H. 1999b. Greedy function approximation: A gradient boosting machine. http://www-stat.stanford.edu/~jhf/ftp/trebst.ps.
10. Friedman, J. H. 2002. Getting started with MART in R. http://www-stat.stanford.edu/~jhf/r-mart/tutorial/tutorial.pdf.
11. Hastie, T., R. Tibshirani, J. Friedman. 2001. The Elements of Statistical Learning. Springer-Verlag, New York.
12. ILOG CPLEX 7.1 Reference Guide. 2001. ILOG CPLEX Division, Incline Village, NV.
13. Johnson, R. A., D. W. Wichern. 1998. Applied Multivariate Statistical Analysis, 4th ed. Prentice-Hall, Englewood Cliffs, NJ.
14. Kim, H., W. Y. Loh. 2000. CRUISE User Manual. Technical Report 989, Department of Statistics, University of Wisconsin, Madison, WI.
15. Kim, H., W. Y. Loh. 2001. Classification tree with unbiased multiway splits. J. Amer. Statist. Assoc. 96 598-604.
16. Loh, W. Y., Y. Shih. 1997. Split selection methods for classification trees. Statistica Sinica 7 815-840.
17. Mangasarian, O. L. 1965. Linear and nonlinear separation of patterns by linear programming. Oper. Res. 13(3) 444-452.
18. Quinlan, R. 1993. C4.5: Programs for Machine Learning. Morgan Kaufman, San Mateo, CA.
19. Ridgeway, G. 2005. Generalized boosted models: A guide to the gbm package. http://i-pensieri.com/gregr/papers/gbm-vignette.pdf.
20. Rifkin, R. 2002. Everything old is new again: A fresh look at historical approaches in machine learning. Ph.D. thesis, Electrical Engineering and Comuter Science and Operations Research, Massachusetts Institute of Technology, Cambridge, MA.
21. Rousseeuw, P. J., A. M. Leroy. 1987. Robust Regression and Outlier Detection. Wiley, New York.
22. Ryan, T. P. 1997. Modern Regression Methods. Wiley Series in Probability and Statistics, John Wiley & Sons, New York.
23. Vapnik, V. 1999. The Nature of Statistical Learning Theory. Springer-Verlag, New York.