# A Minimax Probability Machine for Non-Decomposable Performance Measures

arXiv: https://arxiv.org/abs/2103.00396 · HTML: https://mlsanity.com/paper/2103.00396/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 49 references that are in the map.
- First posted on arXiv 28 Feb 2021.

## Builds on (most cited first, 9 of 9)

- [A systematic study of the class imbalance problem in convolutional neural networks](https://mlsanity.com/paper/1710.05381/) (2017)
- [Imbalanced-learn: A Python Toolbox to Tackle the Curse of Imbalanced Datasets in Machine Learning](https://mlsanity.com/paper/1609.06570/) (2016)
- [Cost Sensitive Learning of Deep Feature Representations from Imbalanced Data](https://mlsanity.com/paper/1508.03422/) (2015)
- [Scalable Learning of Non-Decomposable Objectives](https://mlsanity.com/paper/1608.04802/) (2016)
- [Optimizing Non-decomposable Performance Measures: A Tale of Two Classes](https://mlsanity.com/paper/1505.06812/) (2015)
- [On the Bayes-optimality of F-measure maximizers](https://mlsanity.com/paper/1310.4849/) (2013)
- [Surrogate regret bounds for generalized classification performance metrics](https://mlsanity.com/paper/1504.07272/) (2015)
- [Optimizing Non-decomposable Measures with Deep Networks](https://mlsanity.com/paper/1802.00086/) (2018)
- [Optimal Decision-Theoretic Classification Using Non-Decomposable Performance Metrics](https://mlsanity.com/paper/1505.01802/) (2015)

## Built on by (most cited first, 4 of 4)

- [Training Over-parameterized Models with Non-decomposable Objectives](https://mlsanity.com/paper/2107.04641/) (2021)
- [Principled Algorithms for Optimizing Generalized Metrics in Binary Classification](https://mlsanity.com/paper/2512.23133/) (2025)
- [Online AUC Optimization Based on Second-order Surrogate Loss](https://mlsanity.com/paper/2510.21202/) (2025)
- [Principled Algorithms for Optimizing Generalized Metrics in Multi-Label Learning](https://mlsanity.com/paper/2605.28767/) (2026)

## Abstract (arXiv)

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 Fβ 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 Fβ 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.