Online Regularized Learning Algorithms in RKHS with $β$- and $φ$-Mixing Sequences

• URL: http://arxiv.org/abs/2507.05929v1
• Date: Tue, 08 Jul 2025 12:25:04 GMT
• Title: Online Regularized Learning Algorithms in RKHS with $β$- and $φ$-Mixing Sequences
• Authors: Priyanka Roy, Susanne Saminger-Platz,
• Abstract summary: We study an online regularized learning algorithm in a reproducing Hilbert kernel spaces (RKHS)<n>We analyze a strictly stationary Markov chain, where the dependence structure is characterized by the (phi)- and (beta)-mixing coefficients.
• Score: 1.1510009152620668
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 \(\phi\)- and \(\beta\)-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.

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