A Minimax Probability Machine for Non-Decomposable Performance Measures

TL;DR

This paper introduces MPMF, a novel minimax probability machine tailored for imbalanced classification tasks using non-decomposable measures like F_beta, with effective solutions and kernel extensions demonstrated on real datasets.

Contribution

The paper develops a new minimax probability machine for the F_beta measure, extending it to other non-decomposable measures and providing effective algorithms including kernel methods.

Findings

MPMF effectively handles imbalanced classification with non-decomposable measures.

The model outperforms existing methods on benchmark datasets.

Kernel extension enables nonlinear classification.

Abstract

Imbalanced classification tasks are widespread in many real-world applications. For such classification tasks, in comparison with the accuracy rate, it is usually much more appropriate to use non-decomposable performance measures such as the Area Under the receiver operating characteristic Curve (AUC) and the $F_\beta$ measure as the classification criterion since the label class is imbalanced. On the other hand, the minimax probability machine is a popular method for binary classification problems and aims at learning a linear classifier by maximizing the accuracy rate, which makes it unsuitable to deal with imbalanced classification tasks. The purpose of this paper is to develop a new minimax probability machine for the $F_\beta$ measure, called MPMF, which can be used to deal with imbalanced classification tasks. A brief discussion is also given on how to extend the MPMF model for several other non-decomposable performance measures listed in the paper. To solve the MPMF model effectively, we derive its equivalent form which can then be solved by an alternating descent method to learn a linear classifier. Further, the kernel trick is employed to derive a nonlinear MPMF model to learn a nonlinear classifier. Several experiments on real-world benchmark datasets demonstrate the effectiveness of our new model.