Discussiones Mathematicae Probability and Statistics 25(1) (2005) 103-113

STACKED REGRESSION WITH RESTRICTIONS

Tomasz Górecki

Faculty of Mathematics and Computer Science,
Adam Mickiewicz University,
Umultowska 87, 61-614 Poznań, Poland

e-mail: drizzt@amu.edu.pl

Abstract

When we apply stacked regression to classification we need only discriminant indices which can be negative. In many situations, we want these indices to be positive, e.g., if we want to use them to count posterior probabilities, when we want to use stacked regression to combining classification. In such situation, we have to use leastsquares regression under the constraint bk ł 0, k = 1,2,ź,K. In their earlier work [5], LeBlanc and Tibshirani used an algorithm given in [4]. However, in this paper we use a more general algorithm given in [6].

Keywords: stacked regression, regression with restrictions, mixed regression.

2000 Mathematics Subject Classification: 62H30, 62J05.

References

[1] C. Blake and C. Merz, UCI Repository of Machine Learning Databases, http://www.ics.uci.edu/ mlearn/MLRepository.html, Univeristy of California, Irvine, Department of Information and Computer Sciences.
[2]L. Breiman, Stacked Regression, Machine Learning 24 (1996), 49-64.
[3]A. Chaturvedi and A. Wan, Estimation of Regression Coefficients Subject to Interval Constraints in Models with Non-spherical Errors, Snakhy[`a] 61 series B (1999), 433-442.
[4]J. Lawson and R. Hanson, Solving Least Squares Problems, Prentice-Hall, New Jersey 1974.
[5] M. LeBlanc and R. Tibshirani, Combining Estimates in Regression and Classification, JASA 91 (1996), 1641-1650.
[6]H. Toutenburg and B. Roeder, Minimax-Linear and Theil Estimator forRestricted Regression Coefficients, Statistics 9 (1978), 499-505.
[7]D. Wolpert, Stacked Generalization, Neural Networks 5 (1992), 241-259.

Received 2 March 2005