Markov Chains and Stochastic Stability
Markov Chains and Stochastic Stability
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
| Hi-index | 0.00 |
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.