Online Regularized Learning Algorithms in RKHS with $β$- and $φ$-Mixing Sequences
This work addresses theoretical guarantees for online learning with dependent data, which is incremental as it extends existing analysis to specific mixing conditions.
The paper tackles the problem of analyzing online regularized learning algorithms in reproducing kernel Hilbert spaces under dependent data processes, specifically deriving probabilistic upper bounds and convergence rates for both exponential and polynomial decay of mixing coefficients.
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.