A Minimax Probability Machine for Non-Decomposable Performance Measures
This addresses imbalanced classification tasks where standard accuracy is inadequate, though it is an incremental extension of existing methods.
The paper tackles imbalanced classification by developing a new minimax probability machine (MPMF) optimized for the Fβ measure, showing effectiveness on real-world benchmark datasets.
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 $F_β$ 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 $F_β$ 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.