Ӧ�ø���ͳ�� 2011, 27(6) 597-613 DOI:      ISSN: 1001-4268 CN: 31-1256

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Learning Rates of Empirical Risk Minimization Regression with Beta-Mixing Inputs
Zou Bin,Xu Zongben,Zhang Hai
Hubei University,Xi'an Jiaotong University,Northwest University
Abstract:

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.

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