Online Regularized Learning Algorithms in RKHS with $\beta$- and $\phi$-Mixing Sequences

Priyanka Roy; Susanne Saminger-Platz

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arXiv · 2507.05929

Online Regularized Learning Algorithms in RKHS with $\beta$- and $\phi$-Mixing Sequences

Priyanka Roy·Susanne Saminger-Platz

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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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Priyanka Roy, Susanne Saminger-Platz. 2025-07-08. Online Regularized Learning Algorithms in RKHS with $\beta$- and $\phi$-Mixing Sequences. https://arxiv.org/abs/2507.05929

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