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Concentration Inequalities for Suprema of Empirical Processes with Dependent Data via Generic Chaining with Applications to Statistical Learning

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  • Chiara Amorino
  • Christian Brownlees
  • Ankita Ghosh

Abstract

This paper develops a general concentration inequality for the suprema of empirical processes with dependent data. The concentration inequality is obtained by combining generic chaining with a coupling-based strategy. Our framework accommodates high-dimensional and heavy-tailed (sub-Weibull) data. We demonstrate the usefulness of our result by deriving non-asymptotic predictive performance guarantees for empirical risk minimization in regression problems with dependent data. In particular, we establish an oracle inequality for a broad class of nonlinear regression models and, as a special case, a single-layer neural network model. Our results show that empirical risk minimzaton with dependent data attains a prediction accuracy comparable to that in the i.i.d. setting for a wide range of nonlinear regression models.

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  • Chiara Amorino & Christian Brownlees & Ankita Ghosh, 2025. "Concentration Inequalities for Suprema of Empirical Processes with Dependent Data via Generic Chaining with Applications to Statistical Learning," Papers 2511.00597, arXiv.org.
    • Handle: RePEc:arx:papers:2511.00597
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    References listed on IDEAS

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    1. Florence Merlevède & Magda Peligrad, 2002. "On the Coupling of Dependent Random Variables and Applications," Springer Books, in: Herold Dehling & Thomas Mikosch & Michael Sørensen (ed.), Empirical Process Techniques for Dependent Data, pages 171-193, Springer.
    2. Brownlees, Christian & Guđmundsson, Guđmundur Stefán, 2025. "Performance Of Empirical Risk Minimization For Linear Regression With Dependent Data," Econometric Theory, Cambridge University Press, vol. 41(2), pages 391-420, April.
    3. Peligrad, Magda, 2002. "Some remarks on coupling of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 60(2), pages 201-209, November.
    4. Bogucki, Robert, 2015. "Suprema of canonical Weibull processes," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 253-263.
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