Estimates of the approximation error using rademacher complexity: Learning vector-valued functions

Journal of Inequalities and Applications

Volumn 2008, Issue , 2008, Pages

  Sanguineti, Marcello ^a   Gnecco, Giorgio ^a  

^a UNIVERSITY OF GENOA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 61449255581     PISSN: 10255834     EISSN: 1029242X     Source Type: Journal    
DOI: 10.1155/2008/640758     Document Type: Article

References (38)

1. Krkov V., Sanguineti M., Comparison of worst case errors in linear and neural network approximation IEEE Transactions on Information Theory 2002 48 1 264 275
2. Barron A. R., Narendra K., Neural net approximation Proceedings of the 7th Yale Workshop on Adaptive and Learning Systems May 1992 New Haven, Conn, USA Yale University Press 69 72
3. Barron A. R., Universal approximation bounds for superpositions of a sigmoidal function IEEE Transactions on Information Theory 1993 39 3 930 945
4. Girosi F., Approximation error bounds that use VC-bounds Proceedings of the International Conference on Artificial Neural Networks (ICANN 95) October 1995 Paris, France 295 302
5. Makovoz Y., Uniform approximation by neural networks Journal of Approximation Theory 1998 95 2 215 228
6. Maiorov V. E., On best approximation by ridge functions Journal of Approximation Theory 1999 99 1 68 94
7. Pinkus A., Approximation theory of the MLP model in neural networks Acta Numerica 1999 8 1 143 195
8. Kon M. A., Raphael L. A., Williams D. A., Extending Girosis approximation estimates for functions in Sobolev spaces via statistical learning theory Journal of Analysis and Applications 2005 3 2 67 90
9. Kon M. A., Raphael L. A., Chen G., Lai M.-J., Approximating functions in reproducing kernel Hilbert spaces via statistical learning theory Wavelets and Splines: Athens 2005 2006 Brentwood, Tenn, USA Nashboro Press 271 286 Modern Methods in Mathematics
10. Gnecco G., Sanguineti M., Approximation error bounds via Rademachers complexity Applied Mathematical Sciences 2008 2 14 153 176
11. Krkov V., Sanguineti M., Geometric upper bounds on rates of variable-basis approximation IEEE Transactions on Information Theory 2008 54 12 5681 5688
12. Krkov V., Sanguineti M., Learning with generalization capability by kernel methods of bounded complexity Journal of Complexity 2005 21 3 350 367
13. Krkov V., Sanguineti M., Approximate minimization of the regularized expected error over kernel models Mathematics of Operations Research 2008 33 3 747 756
14. Bellman R., Dynamic Programming 1957 Princeton, NJ, USA Princeton University Press xxv+342
15. Vapnik V. N., The Nature of Statistical Learning Theory 1995 New York, NY, USA Springer xvi+188
16. Aronszajn N., Theory of reproducing kernels Transactions of the American Mathematical Society 1950 68 337 404
17. Buescu J., Paixo A. C., Inequalities for differentiable reproducing kernels and an application to positive integral operators Journal of Inequalities and Applications 2006 2006 9
18. Cucker F., Smale S., On the mathematical foundations of learning Bulletin of the American Mathematical Society 2002 39 1 1 49
19. Berg C., Christensen J. P. R., Ressel P., Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Function 1984 100 New York, NY, USA Springer x+289 Graduate Texts in Mathematics
20. Mendelson S., Mendelson S., Smola A., A few notes on statistical learning theory Advanced Lectures on Machine Learning 2003 2600 Berlin, Germany Springer 1 40 Lecture Notes in Computer Science
21. Blanchard G., Bousquet O., Zwald L., Statistical properties of kernel principal component analysis Machine Learning 2007 66 2-3 259 294
22. Smale S., Zhou D.-X., Shannon sampling and function reconstruction from point values Bulletin of the American Mathematical Society 2004 41 3 279 305
23. Smale S., Zhou D.-X., Learning theory estimates via integral operators and their approximations Constructive Approximation 2007 26 2 153 172
24. Cucker F., Zhou D.-X., Learning Theory: An Approximation Theory Viewpoint 2007 Cambridge, UK Cambridge University Press xii+224 Cambridge Monographs on Applied and Computational Mathematics
25. Bertsekas D. P., Dynamic Programming and Optimal Control. Vol. II 2001 2nd Belmont, Mass, USA Athena Scientific
26. Mussa-Ivaldi F. A., From basis functions to basis fields: vector field approximation from sparse data Biological Cybernetics 1992 67 6 479 489
27. Mussa-Ivaldi F. A., Gandolfo F., Networks that approximate vector-valued mappings 3 Proceedings of IEEE International Conference on Neural Networks (ICNN 93) March-April 1993 San Francisco, Calif, USA 1973 1978
28. Micchelli C. A., Pontil M., On learning vector-valued functions Neural Computation 2005 17 1 177 204
29. Caponnetto A., Micchelli C. A., Pontil M., Ying Y., Universal multi-task kernels Journal of Machine Learning Research 2008 9 1615 1646
30. Rudin W., Real and Complex Analysis 1987 3rd New York, NY, USA McGraw-Hill xiv+416
31. Ong C. S., Mary X., Canu S., Smola A. J., Learning with non positive kernels Proceedings of the 21st International Conference on Machine Learning (ICML 04) July 2004 Banff, Canada 639 646
32. Sontag E., Bishop C., VC dimension of neural networks Neural Networks and Machine Learning 1998 Berlin, Germany Springer 69 95
33. Kolmogorov A. N., Fomn S. V., Introductory Real Analysis 1975 New York, NY, USA Dover xii+403
34. Bartlett P. L., Mendelson S., Rademacher and Gaussian complexities: risk bounds and structural results Journal of Machine Learning Research 2002 3 463 482
35. Mangasarian O. L., Rosen J. B., Thompson M. E., Convex kernel underestimation of functions with multiple local minima Computational Optimization and Applications 2006 34 1 35 45
36. Friedman A., Foundations of Modern Analysis 1982 New York, NY, USA Dover vi+250
37. Montrucchio L., Lipschitz continuous policy functions for strongly concave optimization problems Journal of Mathematical Economics 1987 16 3 259 273
38. Gnecco G., Sanguineti M., Suboptimal solutions to dynamic optimization problems via approximations of the policy functions Journal of Optimization Theory and Applications. to appear