mlsanityData to 7 Oct 2026

Learning with Square Loss: Localization through Offset Rademacher Complexity

arXiv 1502.06134 ↗First posted 21 Feb 2015stat.ML cs.LG math.STcited by 37

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Abstract (arXiv)

We consider regression with square loss and general classes of functions without the boundedness assumption. We introduce a notion of offset Rademacher complexity that provides a transparent way to study localization both in expectation and in high probability. For any (possibly non-convex) class, the excess loss of a two-step estimator is shown to be upper bounded by this offset complexity through a novel geometric inequality. In the convex case, the estimator reduces to an empirical risk minimizer. The method recovers the results of citepRakSriTsy15 for the bounded case while also providing guarantees without the boundedness assumption.

Key facts. Cited by 37 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 Feb 2015.

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Citing papers per year: 2021: 4; 2022: 6; 2023: 6; 2024: 7; 2025: 10; 2026: 4.

37 papers.

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  6. 2021On Empirical Risk Minimization with Dependent and Heavy-Tailed Datacited by 16
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  10. 2022Exponential Tail Local Rademacher Complexity Risk Bounds Without the Bernstein Conditioncited by 9
  11. 2023High-Probability Risk Bounds via Sequential Predictorscited by 9
  12. 2021Localization, Convexity, and Star Aggregationcited by 7
25 more
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  7. 2023On the rate of convergence of an over-parametrized Transformer classifier learned by gradient descentcited by 2
  8. 2025Distribution-dependent Generalization Bounds for Tuning Linear Regression Across Taskscited by 2
  9. 2026Sharper Generalization Bounds for Transformercited by 2
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  11. 2024Guarantees for Nonlinear Representation Learning: Non-identical Covariates, Dependent Data, Fewer Samplescited by 1
  12. 2024On the Efficiency of ERM in Feature Learningcited by 1
  13. 2024Adventures in Demand Analysis Using AIcited by 1
  14. 2025Reweighting Improves Conditional Risk Boundscited by 1
  15. 2025Adaptive Classification of Interval-Valued Time Seriescited by 1
  16. 2026Ratio Covers of Convex Sets and Optimal Mixture Density Estimationcited by 1
  17. 2026Generalization Guarantees on Data-Driven Tuning of Gradient Descent with Langevin Updatescited by 1
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