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 ...
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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.
The previous results describing the generalization ability of Empirical Risk Minimization (erm) algorithm are usually based on the assumption of independent and identically distributed (i.i.d.) samples. In this paper ...
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The previous results describing the generalization ability of Empirical Risk Minimization (erm) algorithm are usually based on the assumption of independent and identically distributed (i.i.d.) samples. In this paper we go far beyond this classical framework by establishing the first exponential bound on the rate of uniform convergence of the erm algorithm with V-geometrically ergodic Markov chain samples, as the application of the bound on the rate of uniform convergence, we also obtain the generalization bounds of the erm algorithm with V-geometrically ergodic Markov chain samples and prove that the erm algorithm with V-geometrically ergodic Markov chain samples is consistent. The main results obtained in this paper extend the previously known results of i.i.d. observations to the case of V-geometrically ergodic Markov chain samples.
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