Support Vector Machine Soft Margin Classifiers: Error Analysis
The Journal of Machine Learning Research
SVM Soft Margin Classifiers: Linear Programming versus Quadratic Programming
Neural Computation
Learning Theory: An Approximation Theory Viewpoint (Cambridge Monographs on Applied & Computational Mathematics)
The performance bounds of learning machines based on exponentially strongly mixing sequences
Computers & Mathematics with Applications
Learning from dependent observations
Journal of Multivariate Analysis
Learning and Generalization: With Applications to Neural Networks
Learning and Generalization: With Applications to Neural Networks
Minimum complexity regression estimation with weakly dependent observations
IEEE Transactions on Information Theory - Part 2
Extension of the PAC framework to finite and countable Markov chains
IEEE Transactions on Information Theory
Capacity of reproducing kernel spaces in learning theory
IEEE Transactions on Information Theory
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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.