{"ID":2897019,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.05929","arxiv_id":"2507.05929","title":"Online Regularized Learning Algorithms in RKHS with $β$- and $φ$-Mixing Sequences","abstract":"In this paper, we study an online regularized learning algorithm in a reproducing kernel Hilbert spaces (RKHS) based on a class of dependent processes. We choose such a process where the degree of dependence is measured by mixing coefficients. As a representative example, we analyze a strictly stationary Markov chain, where the dependence structure is characterized by the \\(φ\\)- and \\(β\\)-mixing coefficients. Under these assumptions, we derive probabilistic upper bounds as well as convergence rates for both the exponential and polynomial decay of the mixing coefficients.","short_abstract":"In this paper, we study an online regularized learning algorithm in a reproducing kernel Hilbert spaces (RKHS) based on a class of dependent processes. We choose such a process where the degree of dependence is measured by mixing coefficients. As a representative example, we analyze a strictly stationary Markov chain,...","url_abs":"https://arxiv.org/abs/2507.05929","url_pdf":"https://arxiv.org/pdf/2507.05929v1","authors":"[\"Priyanka Roy\",\"Susanne Saminger-Platz\"]","published":"2025-07-08T12:25:04Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"math.FA\"]","methods":"[]","has_code":false}