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The previous works describing the generalization ability of learning algorithms are based on independent and identically distributed (i.i.d.) samples. In this paper we go far beyond this classical framework by studying the learning performance of the empirical risk minimization (ERM) algorithm with Markov chain samples. We obtain the bound on the rate of uniform convergence of the ERM algorithm with...
The generalization performance is the important property of learning machines. It has been shown previously by Vapnik, Cucker and Smale, et.al. that, the empirical risks of learning machines based on an i.i.d. sequence must uniformly converge to their expected risks as the number of samples approaches infinity. This paper considers regularization schemes associated with the least square loss and reproducing...
The generalization performance is the important property of learning machines. It has been shown previously by Vapnik, Cucker and Smale that, the empirical risks of learning machine based on i.i.d. sequence must uniformly converge to their expected risks as the number of samples approaches infinity. This paper extends the results to the case where the i.i.d. sequence is replaced by phi-mixing sequence...
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