基于β-混合输入的经验风险最小化回归的学习速率

摘要

研究最小平方损失下的经验风险最小化算法是统计学习理论中非常重要研究内容之一.而以往研究经验风险最小化回归学习速率的几乎所有工作都是基于独立同分布输入假设的.然而,独立的输入样本是一个非常强的条件.因此,在本文,我们超出了独立输入样本这个经典框架来研究了基于β混合输入样本的经验风险最小化回归算法学习速率的界.我们证明了基于β混合输入样本的经验风险最小化回归算法是一致的,指出了本文所建立的结果同样适合输入样本是马氏链、隐马氏链的情形.%The study of empirical risk minimization (ERM) algorithm associated with least squared loss is one of very important issues in statistical learning theory.The main results describing the learning rates of ERM regression are almost based on independent and identically distributed (i.i.d.) inputs.However,independence is a very restrictive concept.In this paper we go far beyond this classical framework by establishing the bound on the learning rates of ERM regression with geometrically β-mixing inputs.We prove that the ERM regression with geometrically β-mixing inputs is consistent and the main results obtained in this paper are also suited to a large class of Markov chains samples and hidden Markov models.