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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationAlgorithmic Learning Theory - 22nd International Conference, ALT 2011, Proceedings
Pages324-337
Number of pages14
DOIs
Publication statusPublished - Oct 20 2011
Event22nd International Conference on Algorithmic Learning Theory, ALT 2011 - Espoo, Finland
Duration: Oct 5 2011Oct 7 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6925 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other22nd International Conference on Algorithmic Learning Theory, ALT 2011
CountryFinland
CityEspoo
Period10/5/1110/7/11

Fingerprint

Margin
Norm
Optimization
Optimization Problem
Classifiers
Classifier
Constant term
Ranking
Sample Size
Maximise

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Suehiro, D., hatano, K., & Takimoto, E. (2011). Approximate reduction from AUC maximization to 1-norm soft margin optimization. In Algorithmic Learning Theory - 22nd International Conference, ALT 2011, Proceedings (pp. 324-337). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6925 LNAI). https://doi.org/10.1007/978-3-642-24412-4_26

Approximate reduction from AUC maximization to 1-norm soft margin optimization. / Suehiro, Daiki; hatano, kohei; Takimoto, Eiji.

Algorithmic Learning Theory - 22nd International Conference, ALT 2011, Proceedings. 2011. p. 324-337 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6925 LNAI).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Suehiro, D, hatano, K & Takimoto, E 2011, Approximate reduction from AUC maximization to 1-norm soft margin optimization. in Algorithmic Learning Theory - 22nd International Conference, ALT 2011, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6925 LNAI, pp. 324-337, 22nd International Conference on Algorithmic Learning Theory, ALT 2011, Espoo, Finland, 10/5/11. https://doi.org/10.1007/978-3-642-24412-4_26
Suehiro D, hatano K, Takimoto E. Approximate reduction from AUC maximization to 1-norm soft margin optimization. In Algorithmic Learning Theory - 22nd International Conference, ALT 2011, Proceedings. 2011. p. 324-337. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-24412-4_26
Suehiro, Daiki ; hatano, kohei ; Takimoto, Eiji. / Approximate reduction from AUC maximization to 1-norm soft margin optimization. Algorithmic Learning Theory - 22nd International Conference, ALT 2011, Proceedings. 2011. pp. 324-337 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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