Learning from uniformly ergodic Markov chains

Journal of Complexity

Volumn 25, Issue 2, 2009, Pages 188-200

  Zou, Bin ^a,b   Zhang, Hai ^a   Xu, Zongben ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b HUBEI UNIVERSITY   (China)

Author keywords

ERM algorithms; Generalization bound; Relative uniform convergence; Uniform convergence; Uniform ergodic Markov chain samples

Indexed keywords

CHAINS; LEARNING SYSTEMS; MARKOV PROCESSES;

EMPIRICAL RISK MINIMIZATION; ERGODIC MARKOV CHAINS; GENERALIZATION BOUND; GENERALIZATION PERFORMANCE; THEORETICAL RESEARCH; UNIFORM CONVERGENCE;

LEARNING ALGORITHMS;

EID: 62549123636     PISSN: 0885064X     EISSN: 10902708     Source Type: Journal    
DOI: 10.1016/j.jco.2009.01.001     Document Type: Article

References (24)

1. Vapnik V. Statistical Learning Theory (1998), John Wiley, New York
2. Bousquet O. New approaches to statistical learning theory. Ann. Inst. Statist. Math. 55 (2003) 371-389
3. Chen D.R., Wu Q., Ying Y.M., and Zhou D.X. Support vector machine soft margin classifiers: Error analysis. J. Mach. Learn. Res. 5 (2004) 1143-1175
4. Cucker F., and Smale S. On the mathematical foundations of learning. Bull. Amer. Math. Soc. 39 (2002) 1-49
5. Cucker F., and Zhou D.X. Learning Theory: An Approximation Theory Viewpoint (2007), Cambridge University Press, Cambridge
6. Smale S., and Zhou D.X. Shannon sampling and function reconstruction from point values. Bull. Amer. Math. Soc. 41 (2004) 279-305
7. Steinwart I., Hush D., and Scovel C. Learning from dependent observations. J. Multivariate Anal. 100 1 (2009) 175-194
8. Yu B. Rates of convergence for empirical processes of stationary mixing sequences. Ann. Probab. 22 (1994) 94-114
9. Modha S., and Masry E. Minimum complexity regression estimation with weakly dependent observations. IEEE Trans. Inform. Theory 42 (1996) 2133-2145
10. Vidyasagar M. Learning and Generalization with Applications to Neural Networks. 2nd edition (2002), Springer, London
11. S. Smale, D.X. Zhou, Online learning with Markov sampling, http://www6.cityu.edu.hk/ma/people/dxzhou/SmaleZhou0708.pdf, 2008
12. Zou B., and Li L.Q. The performance bounds of learning machines based on exponentially strongly mixing sequence. Comput. Math. Appl. 53 7 (2007) 1050-1058
13. Bin Zou, Luoqing Li, Zongben Xu, The generalization performance of ERM algorithm with strongly mixing observations, Mach. Learn. (2009), doi:10.1007/s10994-009-5104-z
14. Andrieu C., Freitas N.de., Doucet A., and Jordan M. An introduction to MCMC learning. Mach. Learn. 50 (2003) 5-43
15. Gilks W.R., and Wild P. Adaptive rejection sampling for Gibbs sampling. Appl. Statist. 51 2 (1992) 337-348
16. Meyn S.P., and Tweedie R.L. Markov Chains and Stochastic Stability (1993), Springer-Verlag
17. Hastings W.K. Monte Carlo sampling methods using Markov chain and their applications. Biometrika 57 (1970) 97-109
18. Jones G.L. On the Markov chain central limit theorem. Probab. Surveys 1 (2004) 299-320
19. Aldous D., Lovász L., and Winkler P. Mixing times for uniformly ergodic Markov chains. Stochastic Process. Appl. 71 (1997) 165-185
20. Glynn P.W., and Ormoneit D. Hoeffding's inequality for uniformly ergodic Markov chains. Statist. Probab. Lett. 56 (2002) 143-146
21. Zhou D.X. Capacity of reproducing kernel spaces in learning theory. IEEE Trans. Inform. Theory 49 (2003) 1743-1752
22. Cucker F., and Smale S. Best choices for regularization parameters in learning theory: On the bias-variance problem. Found. Comput. Math. 2 (2002) 413-428
23. Asmussen S., Glynn P.W., and Thorisson H. Stationarity detection in the initial transient problem. ACM Trans. Model. Comput. Simul. 2 (1992) 130-157
24. Devroye L., Györfi L., and Lugosi G. A Probabilistic Theory of Pattern Recognition (1996), Springer-Verlag, New York