Principled Algorithms for Optimizing Generalized Metrics in Binary Classification
This work addresses a critical problem in machine learning for applications with class imbalance or asymmetric costs, offering a novel framework with provable guarantees, though it builds on existing cost-sensitive learning approaches.
The paper tackles the challenge of optimizing generalized metrics like Fβ-measure and Jaccard similarity in binary classification, particularly for imbalanced or cost-sensitive scenarios, by introducing principled algorithms with theoretical guarantees and demonstrating their effectiveness in experiments.
In applications with significant class imbalance or asymmetric costs, metrics such as the $F_β$-measure, AM measure, Jaccard similarity coefficient, and weighted accuracy offer more suitable evaluation criteria than standard binary classification loss. However, optimizing these metrics present significant computational and statistical challenges. Existing approaches often rely on the characterization of the Bayes-optimal classifier, and use threshold-based methods that first estimate class probabilities and then seek an optimal threshold. This leads to algorithms that are not tailored to restricted hypothesis sets and lack finite-sample performance guarantees. In this work, we introduce principled algorithms for optimizing generalized metrics, supported by $H$-consistency and finite-sample generalization bounds. Our approach reformulates metric optimization as a generalized cost-sensitive learning problem, enabling the design of novel surrogate loss functions with provable $H$-consistency guarantees. Leveraging this framework, we develop new algorithms, METRO (Metric Optimization), with strong theoretical performance guarantees. We report the results of experiments demonstrating the effectiveness of our methods compared to prior baselines.