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arXiv · 2501.02353

Reweighting Improves Conditional Risk Bounds

Yikai Zhang·Jiahe Lin·Fengpei Li·Songzhu Zheng·Anant Raj·Anderson Schneider·Yuriy Nevmyvaka
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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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Yikai Zhang, Jiahe Lin, Fengpei Li, Songzhu Zheng, Anant Raj, Anderson Schneider, Yuriy Nevmyvaka. 2025-01-04. Reweighting Improves Conditional Risk Bounds. https://arxiv.org/abs/2501.02353

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