An improved analysis of the Rademacher data-dependent bound using its self bounding property

Neural Networks

Volumn 44, Issue , 2013, Pages 107-111

  Oneto, Luca ^a   Ghio, Alessandro ^a   Anguita, Davide ^a   Ridella, Sandro ^a  

^a UNIVERSITY OF GENOA   (Italy)

Author keywords

Concentration of measure; Data dependent bounds; Error estimation; Rademacher complexity

Indexed keywords

CONCENTRATION OF MEASURE; DATA DISTRIBUTION; DATA-DEPENDENT BOUNDS; GENERALIZATION ABILITY; MEASURES OF COMPLEXITY; RADEMACHER COMPLEXITY;

COGNITIVE SYSTEMS; ERROR ANALYSIS;

ARTIFICIAL INTELLIGENCE;

ARTICLE; CLASSIFICATION; CLASSIFIER; INTERMETHOD COMPARISON; LEARNING; MATHEMATICAL COMPUTING; PRIORITY JOURNAL; PROBABILITY; RADEMACHER COMPLEXITY;

ARTIFICIAL INTELLIGENCE; STATISTICS AS TOPIC;

EID: 84876310829     PISSN: 08936080     EISSN: 18792782     Source Type: Journal    
DOI: 10.1016/j.neunet.2013.03.017     Document Type: Article

References (24)

1. Anguita, D., Ghio, A., Oneto, L., & Ridella, S. (2011a). Selecting the hypothesis space for improving the generalization ability of support vector machines. In Proceedings of the 2011 IEEE international joint conference on neural networks (IJCNN).
2. Anguita, D., Ghio, A., Oneto, L., & Ridella, S. (2011b). The impact of unlabeled patterns in Rademacher complexity theory for kernel classifiers. In proceedings of neural information processing systems (NIPS).
3. Anguita, D., Ghio, A., Oneto, L., & Ridella, S. (2012). In-sample and out-of-sample model selection and error estimation for support vector machines. IEEE Transactions on Neural Networks and Learning System (in press).
4. Anguita D., Ridella S., Rivieccio F., Zunino R. Quantum optimization for training support vector machines. Neural Networks 2003, 16:763-770.
5. Anthony M. Aspects of discrete mathematics and probability in the theory of machine learning. Discrete Applied Mathematics 2008, 156:883-902.
6. Bartlett P., Boucheron S., Lugosi G. Model selection and error estimation. Machine Learning 2002, 48:85-113.
7. Bartlett P., Bousquet O., Mendelson S. Local Rademacher complexities. The Annals of Statistics 2005, 33:1497-1537.
8. Bartlett P.L., Mendelson S. Rademacher and gaussian complexities: risk bounds and structural results. Journal of Machine Learning Research 2003, 3:463-482.
9. Boucheron S., Lugosi G., Massart P. Concentration inequalities using the entropy method. Annals of Probability 2003, 1583-1614.
10. Boucheron S., Lugosi G., Massart P. A sharp concentration inequality with applications. Random Structures & Algorithms 2000, 16:277-292.
11. Braga-Neto U.M., Dougherty E.R. Is cross-validation valid for small-sample microarray classification?. Bioinformatics 2004, 20:374-380.
12. Casella G., Berger R. Statistical inference 2001, Duxbury Press.
13. Cherkassky V., Shao X., Mulier F.M., Vapnik V.N. Model complexity control for regression using vc generalization bounds. IEEE Transactions on Neural Networks 1999, 10:1075-1089.
14. Giné E., Zinn J. Some limit theorems for empirical processes. The Annals of Probability 1984, 12:929-989.
15. Koltchinskii V. Rademacher penalties and structural risk minimization. IEEE Transactions on Information Theory 2001, 47:1902-1914.
16. Kulkarni S., Lugosi G., Venkatesh S. Learning pattern classification-a survey. IEEE Transactions on Information Theory 1998, 44:2178-2206.
17. Lugosi G. On concentration-of-measure inequalities. Lecture notes 2005.
18. Magdon-Ismail, M. (2010). Permutation complexity bound on out-sample error. In Proceedings of neural information processing systems (NIPS).
19. McDiarmid C. On the method of bounded differences. Surveys in Combinatorics 1989, 141:148-188.
20. Pochet N., Janssens F., De Smet F., Marchal K., Suykens J., De Moor B. M@cbeth: a microarray classification benchmarking tool. Bioinformatics 2005, 21:3185-3186.
21. Shawe-Taylor J., Bartlett P., Williamson R., Anthony M. Structural risk minimization over data-dependent hierarchies. IEEE Transactions on Information Theory 1998, 44:1926-1940.
22. Srebro, N., Sridharan, K., & Tewari, A. (2010). Smoothness, low noise and fast rates. In Proceedings of neural information processing systems (NIPS).
23. Vapnik V. Statistical learning theory 1998, Wiley-Interscience.
24. Vapnik V. An overview of statistical learning theory. IEEE Transactions on Neural Networks 1999, 10:988-999.