2011
DOI: 10.1007/s10444-011-9182-7
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Generalization bounds of ERM algorithm with V-geometrically Ergodic Markov chains

Abstract: 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 Vgeometrically ergodic Markov chain samples, as the application of the bound on the rate of uniform convergence, we also obtain the generalization boun… Show more

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Cited by 10 publications
(8 citation statements)
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“…The proofs in our paper use a previous result on the uniform convergence rate of the empirical loss for V-geometrically ergodic Markov chains [6]. Convergence of the empirical loss is a fundamental problem in statistics and statistical learning theory, and it has been studied for other types of Markov chains such as α-mixing [4,14,15], β-mixing [16,17], φ-mixing [16], and uniformly ergodic [5] chains.…”
Section: Related Workmentioning
confidence: 99%
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“…The proofs in our paper use a previous result on the uniform convergence rate of the empirical loss for V-geometrically ergodic Markov chains [6]. Convergence of the empirical loss is a fundamental problem in statistics and statistical learning theory, and it has been studied for other types of Markov chains such as α-mixing [4,14,15], β-mixing [16,17], φ-mixing [16], and uniformly ergodic [5] chains.…”
Section: Related Workmentioning
confidence: 99%
“…We now introduce the V-geometrically ergodic Markov chains and the settings for our analyses. We will follow the definitions in [6]. We also review a result on the uniform convergence rate of the empirical loss for V-geometrically ergodic Markov data [6] which will be used in the subsequent sections.…”
Section: Preliminariesmentioning
confidence: 99%
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