Reweighting Improves Conditional Risk Bounds

• URL: http://arxiv.org/abs/2501.02353v1
• Date: Sat, 04 Jan 2025 18:16:21 GMT
• Title: Reweighting Improves Conditional Risk Bounds
• Authors: Yikai Zhang, Jiahe Lin, Fengpei Li, Songzhu Zheng, Anant Raj, Anderson Schneider, Yuriy Nevmyvaka,
• Abstract summary: We show that under a general balanceable" Bernstein condition, one can design a weighted ERM estimator to achieve superior performance in certain sub-regions.<n>Our findings are supported by evidence from synthetic data experiments.
• Score: 12.944919903533957
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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