TY - GEN

T1 - Approximate reduction from AUC maximization to 1-norm soft margin optimization

AU - Suehiro, Daiki

AU - Hatano, Kohei

AU - Takimoto, Eiji

N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011

Y1 - 2011

N2 - Finding linear classifiers that maximize AUC scores is important in ranking research. This is naturally formulated as a 1-norm hard/soft margin optimization problem over pn pairs of p positive and n negative instances. However, directly solving the optimization problems is impractical since the problem size (pn) is quadratically larger than the given sample size (p+n). In this paper, we give (approximate) reductions from the problems to hard/soft margin optimization problems of linear size. First, for the hard margin case, we show that the problem is reduced to a hard margin optimization problem over p+n instances in which the bias constant term is to be optimized. Then, for the soft margin case, we show that the problem is approximately reduced to a soft margin optimization problem over p+n instances for which the resulting linear classifier is guaranteed to have a certain margin over pairs.

AB - Finding linear classifiers that maximize AUC scores is important in ranking research. This is naturally formulated as a 1-norm hard/soft margin optimization problem over pn pairs of p positive and n negative instances. However, directly solving the optimization problems is impractical since the problem size (pn) is quadratically larger than the given sample size (p+n). In this paper, we give (approximate) reductions from the problems to hard/soft margin optimization problems of linear size. First, for the hard margin case, we show that the problem is reduced to a hard margin optimization problem over p+n instances in which the bias constant term is to be optimized. Then, for the soft margin case, we show that the problem is approximately reduced to a soft margin optimization problem over p+n instances for which the resulting linear classifier is guaranteed to have a certain margin over pairs.

UR - http://www.scopus.com/inward/record.url?scp=80054091131&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80054091131&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-24412-4_26

DO - 10.1007/978-3-642-24412-4_26

M3 - Conference contribution

AN - SCOPUS:80054091131

SN - 9783642244117

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 324

EP - 337

BT - Algorithmic Learning Theory - 22nd International Conference, ALT 2011, Proceedings

T2 - 22nd International Conference on Algorithmic Learning Theory, ALT 2011

Y2 - 5 October 2011 through 7 October 2011

ER -