Online Regularized Statistical Learning in Reproducing Kernel Hilbert Space With Non-Stationary Data

[2404.03211] Online Regularized Statistical Learning in Reproducing Kernel Hilbert Space With Non-Stationary Data Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2404.03211 (cs) [Submitted on 4 Apr 2024 ( v1 ), last revised 17 Aug 2026 (this version, v7)] Title: Online Regularized Statistical Learning in Reproducing Kernel Hilbert Space With Non-Stationary Data Authors: Yan Chen , Tao Li , Xiwei Zhang View a PDF of the paper titled Online Regularized Statistical Learning in Reproducing Kernel Hilbert Space With Non-Stationary Data, by Yan Chen and 1 other authors View PDF HTML (experimental) Abstract: We study recursive regularized learning algorithms in the reproducing kernel Hilbert space (RKHS) with non-stationary online data streams. We introduce the concept of a random Tikhonov regularization path and decompose the tracking error of the algorithm's output for the regularization path into random difference equations in RKHS. We show that the tracking error vanishes in mean square and almost surely if the regularization path is slowly time-varying. Then, leveraging the monotonicity of inverse operators and the spectral decomposition of compact operators, and introducing the RKHS persistence of excitation condition, we develop a dominated convergence method to prove the mean square and almost sure consistency between the regularization path and the unknown function to be learned. Especially, for independent and non-identically distributed data streams, the mean square and almost sure consistency between the algorithm's output and the unknown function is achieved if the input data's marginal probability measures are slowly time-varying and the average measure over each fixed-length time period is uniformly above a strictly positive finite Borel measure. Subjects: Machine Learning (cs.LG) ; Systems and Control (eess.SY) Cite as: arXiv:2404.03211 [cs.LG] (or arXiv:2404.03211v7 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2404.03211 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Tao Li [ view email ] [v1] Thu, 4 Apr 2024 05:35:59 UTC (149 KB) [v2] Sun, 26 May 2024 10:09:37 UTC (149 KB) [v3] Wed, 29 May 2024 11:48:59 UTC (149 KB) [v4] Sun, 9 Jun 2024 13:11:36 UTC (149 KB) [v5] Tue, 23 Sep 2025 06:21:41 UTC (211 KB) [v6] Thu, 23 Oct 2025 08:32:49 UTC (223 KB) [v7] Mon, 17 Aug 2026 02:15:48 UTC (1,687 KB) Full-text links: Access Paper: View a PDF of the paper titled Online Regularized Statistical Learning in Reproducing Kernel Hilbert Space With Non-Stationary Data, by Yan Chen and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2024-04 Change to browse by: cs cs.SY eess eess.SY References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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