Lower bounds for the empirical minimization algorithm

IEEE Transactions on Information Theory

Volumn 54, Issue 8, 2008, Pages 3797-3803

  Mendelson, Shahar ^a,b  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Empirical minimization; Function learning; Lower bounds; Statistical learning theory

Indexed keywords

CONTROL THEORY; ERROR ANALYSIS; LEARNING SYSTEMS;

CLASS-F; EMPIRICAL MINIMIZATION; ERROR RATE; FUNCTION LEARNING; FUNCTIONALS; LOWER BOUNDS; MINIMIZATION ALGORITHMS; STATISTICAL LEARNING THEORY; TARGET FUNCTIONS;

LEARNING ALGORITHMS;

EID: 48849092018     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2008.926323     Document Type: Article

References (22)

1. M. Anthony and P. L. Bartlett, Neural Network Learning: Theoretical Foundations. Cambridge, U.K.: Cambridge Univ. Press, 1999.
2. P. L. Bartlett, O. Bousquet, and S. Mendelson, "Local Rademacher complexities," Ann. Statist., vol. 33, no. 4, pp. 1497-1537, 2005.
3. P. L. Bartlett and S. Mendelson, "Empirical minimization," Probab. Theory Related Fields, vol. 135, pp. 311-334, 2006.
4. S. Boucheron, O. Bousquet, and G. Lugosi, "Theory of classification: A Survey of recent advances," ESAIM: Probab. Statist., vol. 9, pp. 323-375, 2005.
5. O. Bousquet, "Concentration inequalities and empirical processes theory applied to the analysis of learning algorithms," Ph.D. dissertation, Dept. Comput. Sci., Ecole Polytechnique, Palaiseau, France, 2002.
6. R. Deville, G. Godefroy, and V. Zizler, Smoothness and Renorming in Banach Spaces. New York: Wiley, 1993.
7. L. Devroye, L. Györfi, and G. Lugosi, A Probabilistic Theory of Pattern Recognition. New York: Springer-Verlag, 1996.
8. J. Diestel, "Sequences and series in Banach spaces," in Graduate Text in Mathematics. Berlin, Germany: Springer-Verlag, 1984, vol. 92.
9. R. M. Dudley, Uniform Central Limit Theorems. Cambridge, U.K.: Cambridge Univ. Press, 1999.
10. P. Habala, P. Hajek, and V. Zizler, Introduction to Banach Spaces. Prague, Czech Republic: Univ. Karlovy, Matfyzpress, 1996, vol. I and II.
11. E. Giné and J. Zinn, "Some limit theorems for empirical processes," Ann. Probab., vol. 12, no. 4, pp. 929-989, 1984.
12. L. Györfi, M. Kohler, A. Krzyzak, and H. Walk, A Distribution-Free Theory of Nonparametric Regression, ser. Statistics. Berlin, Germany: Springer-Verlag, 2002.
13. M. Ledoux and M. Talagrand, Probability in Banach Spaces: Isoperimetry and Processes. New York: Springer-Verlag, 1991.
14. G. Lugosi, "Pattern classification and learning theory," in Principles of Nonparametric Learning, L.Györfi, Ed. New York: Springer-Verlag, 2002, pp. 1-56.
15. W. S. Lee, P. L. Bartlett, and R. C. Williamson, "The importance of convexity in learning with squared loss," IEEE Trans. Inf. Theory vol. 44, no. 5, pp. 1974-1980, Sep. 1998.
16. W. S. Lee, P. L. Bartlett, and R. C. Williamson, "Correction to "The importance of convexity in learning with squared loss"," 2008, prepint.
17. S. Mendelson, "Improving the sample complexity using global data," IEEE Trans. Inf. Theory, vol. 48, no. 7, pp. 1977-1991, Jul. 2002.
18. S. Mendelson, "Geometric parameters in learning theory," in GAFA Lecture Notes. Berlin, Germany: Springer-Verlag, 2004, vol. 1850, LNM, pp. 193-236.
19. S. Mendelson, "Obtaining fast error rates in nonconvex situations," J. Complexity, to be published.
20. D. Stroock, Probability Theory, an Analytic View. Cambridge, U.K.: Cambridge Univ. Press, 1993.
21. S. van de Geer, Empirical Processes in M-Estimation. Cambridge, U.K.: Cambridge Univ. Press, 2000.
22. A. W. Van der Vaart and J. A.Wellner, Weak Convergence and Empirical Processes. New York: Springer-Verlag, 1996.