Concentration Inequalities for Suprema of Empirical Processes with Dependent Data via Generic Chaining with Applications to Statistical Learning
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918346792894464 |
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| author | Amorino, Chiara Brownlees, Christian Ghosh, Ankita |
| author_facet | Amorino, Chiara Brownlees, Christian Ghosh, Ankita |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00597 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Concentration Inequalities for Suprema of Empirical Processes with Dependent Data via Generic Chaining with Applications to Statistical Learning Amorino, Chiara Brownlees, Christian Ghosh, Ankita Econometrics 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. |
| title | Concentration Inequalities for Suprema of Empirical Processes with Dependent Data via Generic Chaining with Applications to Statistical Learning |
| topic | Econometrics |
| url | https://arxiv.org/abs/2511.00597 |