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This research addresses the limitations of standard accuracy in imbalanced binary classification by introducing exact constrained reformulations for direct metric optimization problems like fixing precision to optimize recall. By replacing smooth approximations with rigorous mathematical formulations solvable via exact penalty methods, this approach offers a more robust framework than current state-of-the-art techniques that rely on balanced accuracy averages. The work provides a significant methodological advance for practitioners needing precise control over specific performance metrics in skewed data distributions rather than just overall balance.
Exact Reformulation and Optimization for Direct Metric Optimization in Binary Imbalanced Classification
arXiv:2507.15240v2 Announce Type: replace Abstract: 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 $F_1$-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.
Abstract: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 $F_1$-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 this https URL.
Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2507.15240 [cs.LG]
(or arXiv:2507.15240v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2507.15240 Focus to learn more arXiv-issued DOI via DataCite
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