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

Chiara Amorino, Christian Brownlees, Ankita Ghosh

arXiv 1 Nov 2025 · Econometrics

arXiv:2511.00597 · PDF · DOI · OpenAlex · Extracted main text

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.

Citation extraction

22
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in-text mentions
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distinct cited
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Michel Talagrand (2005) The Generic Chaining: Upper and Lower Bounds of Stochastic Processes0.9285480%
2Brownlees, C. and Gudmundsson, G. S (2025) Performance of Empirical Risk Minimization for Linear Regression with Dependent Data self0.92843100%
3Brownlees, C. and Llorens-Terrazas, J (2025) Empirical Risk Minimization for Time Series: Nonparametric Performance Bounds for Prediction self0.92843100%
4Merlevède, Florence and Peligrad, Magda (2002) On the Coupling of Dependent Random Variables and Applications0.8435360%
5Jiang, Wenxin and Tanner, Martin (2010) Risk Minimization for Time Series Binary Choice with Variable Selection0.84333100%
6Boucheron, S. and Lugosi, G. and Massart, P (2013) Concentration Inequalities: A Nonasymptotic Theory of Independence0.7373367%
7Devroye, L. and Györfi, L. and Lugosi, G (1996) A Probabililstic Theory of Pattern Recognition0.73732100%
8Doukhan, Paul (1994) Mixing0.64422100%
9Vershynin, Roman (2026) High-Dimensional Probability: An Introduction with Applications in Data Science0.5114225%
10Kuchibhotla, Arun Kumar and Chakrabortty, Abhishek (2022) Moving beyond sub-Gaussianity in high-dimensional statistics: applications in covariance estimation and linear regression0.5113233%

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Cited by, within the corpus

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