Bennett-type generalization bounds: Large-deviation case and faster rate of convergence

Uncertainty in Artificial Intelligence - Proceedings of the 29th Conference, UAI 2013

Volumn , Issue , 2013, Pages 714-722

  Zhang, Chao ^a  

^a ARIZONA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DEVIATION INEQUALITIES; EMPIRICAL RISKS; EXPECTED RISK; FASTER RATES; GENERALIZATION BOUND; LEARNING PROCESS; RADEMACHER COMPLEXITY;

ARTIFICIAL INTELLIGENCE; LEARNING SYSTEMS;

APPROXIMATION THEORY;

EID: 84888140677     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (14)

1. P.L. Bartlett, O. Bousquet, and S. Mendelson. Local rademacher complexities. Annals of Statistics, 33 (4): 1497-1537, 2005.
2. S. Ben-David, J. Blitzer, K. Crammer, A. Kulesza, F. Pereira, and J.W. Vaughan. A theory of learning from different domains. Machine Learning, 79(1): 151-175, 2010.
3. G. Bennett. Probability inequalities for the sum of independent random variables. Journal of the American Statistical Association, 57(297): 33-45, 1962.
4. A. Blumer, A. Ehrenfeucht, D. Haussler, and M. Warmuth. Learnability and the vapnik-chervonenkis dimension. Journal of the ACM, 36(4): 929-965, 1989.
5. O. Bousquet. A bennett concentration inequality and its application to suprema of empirical processes. Comptes Rendus Mathematique, 334(6): 495-500, 2002.
6. O. Bousquet, S. Boucheron, and G. Lugosi. Introduction to statistical learning theory. Advanced Lectures on Machine Learning, pages 169-207, 2004.
7. W. Hoeffding. Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association, 58(301): 13-30, 1963.
8. R. Latala. Sudakov minoration principle and supremum of some processes. Geometric & Functional Analysis GAFA, 7(5): 936-953, 1997.
9. S. Mendelson. A few notes on statistical learning theory. Advanced Lectures on Machine Learning, pages 1-40, 2003.
10. M. Mohri and A. Rostamizadeh. Stability bounds for stationary φ-mixing and β-mixing processes. Journal of Machine Learning Research, 11: 798-814, 2010.
11. Michel Talagrand. Constructions of majorizing measures bernoulli processes and cotype. Geometric & Functional Analysis GAF A, 4(6): 660-717, 1994a.
12. Michel Talagrand. The supremum of some canonical processes. American Journal of Mathematics, 116 (2): 283-325, 1994b.
13. A. Van der Vaart and J. Wellner. Weak Convergence and Empirical Processes: with Aapplications to Statistics. Springer, 1996.
14. V.N. Vapnik. Statistical Learning Theory. Wiley, 1998.