研究在依赖数据下在线正则化学习的收敛性与误差边界。
Online Regularized Learning Algorithms in RKHS with $β$- and $ϕ$-Mixing Sequences
- 基于混洗系数分析依赖数据中的在线学习方法。
- 给出指数与多项式衰减下的概率上界和收敛速率。
- 适合关注机器学习泛化理论的研究者阅读。
本文研究了在再生核希尔伯特空间（RKHS）中基于一类依赖过程的在线正则化学习算法。选择以混洗系数衡量依赖程度的过程，以严格平稳马尔可夫链为例，其依赖结构由ϕ-和β-混洗系数刻画。在这些假设下，推导了混合系数指数与多项式衰减情况下的概率上界及收敛速率。
原文摘要 · Abstract (English)
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.
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