Regularized least square regression with dependent samples

In this paper we study the learning performance of regularized least square regression with α-mixing and ϕ-mixing inputs. The capacity independent error bounds and learning rates are derived by means of an integral operator technique. Even for independent samples our learning rates improve those in the literature. The results are sharp in the sense that when the mixing conditions are strong enough the rates are shown to be close to or the same as those for learning with independent samples. They also reveal interesting phenomena of learning with dependent samples: (i) dependent samples contain less information and lead to worse error bounds than independent samples; (ii) the influence of the dependence between samples to the learning process decreases as the smoothness of the target function increases.