Stacked regression with restrictions

Tomasz Górecki

Discussiones Mathematicae Probability and Statistics (2005)

  • Volume: 25, Issue: 1, page 103-113
  • ISSN: 1509-9423

Abstract

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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].

How to cite

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Tomasz Górecki. "Stacked regression with restrictions." Discussiones Mathematicae Probability and Statistics 25.1 (2005): 103-113. <http://eudml.org/doc/287721>.

@article{TomaszGórecki2005,
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 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].},
author = {Tomasz Górecki},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {stacked regression; regression with restrictions; mixed regression},
language = {eng},
number = {1},
pages = {103-113},
title = {Stacked regression with restrictions},
url = {http://eudml.org/doc/287721},
volume = {25},
year = {2005},
}

TY - JOUR
AU - Tomasz Górecki
TI - Stacked regression with restrictions
JO - Discussiones Mathematicae Probability and Statistics
PY - 2005
VL - 25
IS - 1
SP - 103
EP - 113
AB - 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].
LA - eng
KW - stacked regression; regression with restrictions; mixed regression
UR - http://eudml.org/doc/287721
ER -

References

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  1. [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. [2] L. Breiman, Stacked Regression, Machine Learning 24 (1996), 49-64. Zbl0849.68104
  3. [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. [4] J. Lawson and R. Hanson, Solving Least Squares Problems, Prentice-Hall, New Jersey 1974. Zbl0860.65028
  5. [5] M. LeBlanc and R. Tibshirani, Combining Estimates in Regression and Classification, JASA 91 (1996), 1641-1650. Zbl0881.62046
  6. [6] H. Toutenburg and B. Roeder, Minimax-Linear and Theil Estimator forRestricted Regression Coefficients, Statistics 9 (1978), 499-505. 
  7. [7] D. Wolpert, Stacked Generalization, Neural Networks 5 (1992), 241-259. 

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