DMCA
Solving a Mixed-Integer Programming Formulation of a Multi-Category Constrained Discrimination Model 1 Abstract
BibTeX
@MISC{Brooks_solvinga,
author = {J Paul Brooks and Eva K Lee},
title = {Solving a Mixed-Integer Programming Formulation of a Multi-Category Constrained Discrimination Model 1 Abstract},
year = {}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
In classification, even if a Bayes-optimal rule has been developed, intergroup misclassification rates may be higher than desirable. We consider a two-stage model for multi-category constrained discrimination in which limits on misclassification rates of training observations may be pre-specified. The mechanism by which the misclassification limits are satisfied is a rejection option, also known as a reserved judgment group, for observations not demonstrating properties of membership to any of the groups. The first stage of the constrained discrimination model involves estimating conditional group density function values for training observations, and the second stage requires the solution of a mixed-integer program (MIP). The MIP is used to estimate the parameters that characterize an optimal classification rule. The MIP is difficult to solve due to the formulation of constraints wherein certain variables are equal to the maximum of linear functions. Solution methods for the MIP are presented, including techniques for generating and exploiting edges of the conflict graph. Improvement in computation times over industrystandard software is demonstrated. 2
Keyphrases
mixed-integer programming formulation multi-category constrained discrimination model training observation certain variable industrystandard software constrained discrimination model conflict graph linear function bayes-optimal rule multi-category constrained discrimination rejection option misclassification limit conditional group density function value two-stage model mixed-integer program computation time reserved judgment group solution method second stage misclassification rate first stage intergroup misclassification rate optimal classification rule
