# Exact Reformulation and Optimization for Direct Metric Optimization in Binary Imbalanced Classification

arXiv: https://arxiv.org/abs/2507.15240 · HTML: https://mlsanity.com/paper/2507.15240/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 89 references that are in the map.
- First posted on arXiv 21 Jul 2025.

## Builds on (most cited first, 30 of 48)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [CheXpert: A Large Chest Radiograph Dataset with Uncertainty Labels and Expert Comparison](https://mlsanity.com/paper/1901.07031/) (2019)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [EDA: Easy Data Augmentation Techniques for Boosting Performance on Text Classification Tasks](https://mlsanity.com/paper/1901.11196/) (2019)
- [Skin Lesion Analysis Toward Melanoma Detection: A Challenge at the 2017 International Symposium on Biomedical Imaging (ISBI), Hosted by the International Skin Imaging Collaboration (ISIC)](https://mlsanity.com/paper/1710.05006/) (2017)
- [Deep learning: a statistical viewpoint](https://mlsanity.com/paper/2103.09177/) (2021)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [Fit without fear: remarkable mathematical phenomena of deep learning through the prism of interpolation](https://mlsanity.com/paper/2105.14368/) (2021)
- [Tilted Empirical Risk Minimization](https://mlsanity.com/paper/2007.01162/) (2020)
- [AUC Maximization in the Era of Big Data and AI: A Survey](https://mlsanity.com/paper/2203.15046/) (2022)
- [Smooth-AP: Smoothing the Path Towards Large-Scale Image Retrieval](https://mlsanity.com/paper/2007.12163/) (2020)
- [Unified Focal loss: Generalising Dice and cross entropy-based losses to handle class imbalanced medical image segmentation](https://mlsanity.com/paper/2102.04525/) (2021)
- [Combo Loss: Handling Input and Output Imbalance in Multi-Organ Segmentation](https://mlsanity.com/paper/1805.02798/) (2018)
- [A Survey on Long-Tailed Visual Recognition](https://mlsanity.com/paper/2205.13775/) (2022)
- [Optimizing Rank-based Metrics with Blackbox Differentiation](https://mlsanity.com/paper/1912.03500/) (2019)
- [Two-Player Games for Efficient Non-Convex Constrained Optimization](https://mlsanity.com/paper/1804.06500/) (2018)
- [Training Well-Generalizing Classifiers for Fairness Metrics and Other Data-Dependent Constraints](https://mlsanity.com/paper/1807.00028/) (2018)
- [Recall@k Surrogate Loss with Large Batches and Similarity Mixup](https://mlsanity.com/paper/2108.11179/) (2021)
- [Scalable Learning of Non-Decomposable Objectives](https://mlsanity.com/paper/1608.04802/) (2016)
- [Stochastic Optimization of Areas Under Precision-Recall Curves with Provable Convergence](https://mlsanity.com/paper/2104.08736/) (2021)
- [Analyzing Overfitting under Class Imbalance in Neural Networks for Image Segmentation](https://mlsanity.com/paper/2102.10365/) (2021)
- [SoDeep: a Sorting Deep net to learn ranking loss surrogates](https://mlsanity.com/paper/1904.04272/) (2019)
- [Boosted Conformal Prediction Intervals](https://mlsanity.com/paper/2406.07449/) (2024)
- [AP-Loss for Accurate One-Stage Object Detection](https://mlsanity.com/paper/2008.07294/) (2020)
- [sigmoidF1: A Smooth F1 Score Surrogate Loss for Multilabel Classification](https://mlsanity.com/paper/2108.10566/) (2021)
- [Complexity of Single Loop Algorithms for Nonlinear Programming with Stochastic Objective and Constraints](https://mlsanity.com/paper/2311.00678/) (2023)
- [GENO -- GENeric Optimization for Classical Machine Learning](https://mlsanity.com/paper/1905.13587/) (2019)
- [Selective Classification Under Distribution Shifts](https://mlsanity.com/paper/2405.05160/) (2024)
- [Variance-reduced first-order methods for deterministically constrained stochastic nonconvex optimization with strong convergence guarantees](https://mlsanity.com/paper/2409.09906/) (2024)

## Built on by (most cited first, 2 of 2)

- [Partial VOROS: A Cost-aware Performance Metric for Binary Classifiers with Precision and Capacity Constraints](https://mlsanity.com/paper/2510.18520/) (2025)
- [A Systematic Evaluation of Imbalance Handling Methods in Biomedical Binary Classification](https://mlsanity.com/paper/2605.14147/) (2026)

## Abstract (arXiv)

For classification with imbalanced class frequencies, i.e., imbalanced classification (IC), standard accuracy is known to be misleading as a performance measure. While most existing methods for IC resort to optimizing balanced accuracy (i.e., the average of class-wise recalls), they fall short in scenarios where the significance of classes varies or certain metrics should reach prescribed levels. In this paper, we study two key classification metrics, precision and recall, under three practical binary IC settings: fix precision optimize recall (FPOR), fix recall optimize precision (FROP), and optimize F1-score (OFOS). Unlike existing methods that rely on smooth approximations to deal with the indicator function involved, we introduce, for the first time, exact constrained reformulations for these direct metric optimization (DMO) problems, which can be effectively solved by exact penalty methods. Experiment results on multiple benchmark datasets demonstrate the practical superiority of our approach over the state-of-the-art methods for the three DMO problems. We also expect our exact reformulation and optimization (ERO) framework to be applicable to a wide range of DMO problems for binary IC and beyond. Our code is available at https://github.com/sun-umn/DMO.