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 βₖ ≥ 0, k = 1,2,...,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].
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1064,
author = {Tomasz G\'orecki},
title = {Stacked regression with restrictions},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {25},
year = {2005},
pages = {103-113},
zbl = {1102.62065},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1064}
}
Tomasz Górecki. Stacked regression with restrictions. Discussiones Mathematicae Probability and Statistics, Tome 25 (2005) pp. 103-113. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1064/
[000] [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.
[001] [2] L. Breiman, Stacked Regression, Machine Learning 24 (1996), 49-64. | Zbl 0849.68104
[002] [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.
[003] [4] J. Lawson and R. Hanson, Solving Least Squares Problems, Prentice-Hall, New Jersey 1974. | Zbl 0860.65028
[004] [5] M. LeBlanc and R. Tibshirani, Combining Estimates in Regression and Classification, JASA 91 (1996), 1641-1650. | Zbl 0881.62046
[005] [6] H. Toutenburg and B. Roeder, Minimax-Linear and Theil Estimator forRestricted Regression Coefficients, Statistics 9 (1978), 499-505.
[006] [7] D. Wolpert, Stacked Generalization, Neural Networks 5 (1992), 241-259.