Generalization Performance of ERM Algorithm with Geometrically Ergodic Markov Chain Samples
ABSTRACT 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 geometrically ergodic Markov chain samples, as an application of our main result we establish the bounds on the generalization performance of the ERM algorithm, and show that the ERM algorithm with geometrically ergodic Markov chain samples is consistent. These results obtained in this paper extend the previously known results of i.i.d. observations to the case of Markov dependent samples.
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ABSTRACT: One of the main goals of machine learning is to study the generalization performance of learning algorithms. The previous main results describing the generalization ability of learning algorithms are usually based on independent and identically distributed (i.i.d.) samples. However, independence is a very restrictive concept for both theory and real-world applications. In this paper we go far beyond this classical framework by establishing the bounds on the rate of relative uniform convergence for the Empirical Risk Minimization (ERM) algorithm with uniformly ergodic Markov chain samples. We not only obtain generalization bounds of ERM algorithm, but also show that the ERM algorithm with uniformly ergodic Markov chain samples is consistent. The established theory underlies application of ERM type of learning algorithms. Keywordsgeneralization bounds–ERM algorithm–relative uniform convergence–uniformly ergodic Markov chain–learning theoryActa Mathematicae Applicatae Sinica 01/2014; 30(1):1-16. DOI:10.1007/s10255-011-0096-4 · 0.38 Impact Factor