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

TL;DR

This paper investigates online regularized learning algorithms in RKHS with dependent data modeled by eta- and \phi-mixing sequences, providing convergence rates and probabilistic bounds for such processes.

Contribution

It introduces a framework for analyzing online learning algorithms in RKHS with dependent data characterized by mixing coefficients, extending prior work to dependent processes.

Findings

Derived probabilistic upper bounds for dependent processes.

Established convergence rates for exponential and polynomial mixing decay.

Analyzed dependence structures via \\phi- and \\beta-mixing coefficients.

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.