2025/01/04 by Yikai Zhang, Jiahe Lin, Zhang, Yikai +11 · 1 citation
Computer Science · Mathematics · #Explainable Artificial Intelligence (XAI) #FOS: Computer and information sciences #G.3 #I.3 #Imbalanced Data Classification Techniques #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2501.02353
openalex publication_date 2025/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we study the weighted empirical risk minimization (weighted ERM) schema, in which an additional data-dependent weight function is incorporated when the empirical risk function is being minimized. We show that under a general ``balanceable" Bernstein condition, one can design a weighted ERM estimator to achieve superior performance in certain sub-regions over the one obtained from standard ERM, and the superiority manifests itself through a data-dependent constant term in the error bound. These sub-regions correspond to large-margin ones in classification settings and low-variance ones in heteroscedastic regression settings, respectively. Our findings are supported by evidence from synthetic data experiments.