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

2025/11/01 by Amorino, Chiara, Brownlees, Christian, Ghosh, Ankita
#Econometrics (econ.EM) #FOS: Economics and business

paper · doi:10.48550/arxiv.2511.00597

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.

Citations

• Empirical Risk Minimization for Time Series: Nonparametric Performance Bounds for Prediction

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