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. © 2011 Springer-Verlag.
CITATION STYLE
Suehiro, D., Hatano, K., & Takimoto, E. (2011). Approximate reduction from AUC maximization to 1-norm soft margin optimization. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6925 LNAI, pp. 324–337). https://doi.org/10.1007/978-3-642-24412-4_26
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