Learning Rates of Empirical Risk Minimization Regression with Beta-Mixing Inputs

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 -mixing inputs. We prove that the ERM regression with geometrically -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.