Uniform approximation of functions with random bases

46th Annual Allerton Conference on Communication, Control, and Computing

Volumn , Issue , 2008, Pages 555-561

  Rahimi, Ali ^a   Recht, Benjamin ^b  

^a INTEL RESEARCH   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COSTS; CONTINUOUS FUNCTIONS; ERROR BOUNDS; FUNCTION FITTINGS; MACHINE LEARNING ALGORITHMS; NON LINEARITIES; NON-LINEAR FUNCTIONS; RANDOM NETWORKS; REPRODUCING KERNEL HILBERT SPACES; UNIFORM APPROXIMATIONS;

BANACH SPACES; HILBERT SPACES; LEARNING SYSTEMS; NONLINEAR NETWORKS; PATTERN RECOGNITION; TOPOLOGY;

LEARNING ALGORITHMS;

EID: 64549160240     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ALLERTON.2008.4797607     Document Type: Conference Paper

References (24)

1. H. D. Block, "The perceptron: a model for brain functioning," Review of modern physics, vol. 34, pp. 123-135, Jan. 1962.
2. Y. Amit and D. Geman, "Shape quantization and recognition with randomized trees," Neural Computation, vol. 9, no. 7, pp. 1545-1588, 1997.
3. F. Moosmann, B. Triggs, and F. Jurie, "Randomized clustering forests for building fast and discriminative visual vocabularies," in Advances in Neural Information Processing Systems (NIPS), 2006.
4. A. Rahimi and B. Recht, "Random features for large-scale kernel machines," in Advances in Neural Information Processing Systems (NIPS), 2007.
5. W. Maass and H. Markram, "On the computational power of circuits of spiking neurons," Journal of Computer and System Sciences, vol. 69, pp. 593-616, Dec. 2004.
6. L. K. Jones, "A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training," The Annals of Statistics, vol. 20, no. 1, pp. 608-613, Mar. 1992.
7. A. Barron, "Universal approximation bounds for superpositions of a sigmoidal function," IEEE Transactions on Information Theory, vol. 39, pp. 930-945, May 1993.
8. A. R. Barron, "Neural net approximation," in Proceedings of the 7th Yale Workshop on Adaptive and Learning Systems, K. S. Narendra, Ed., 1992, pp. 69-72.
9. F. Girosi, "Approximation error bounds that use VC-bounds," in International Conference on Neural Networks, 1995, pp. 295-302.
10. G. Gnecco and M. Sanguineti, "Approximation error bounds via Rademacher's complexity," Applied Mathematical Sciences, vol. 2, no. 4, pp. 153-176, 2008.
11. R. E. Schapire, "The boosting approach to machine learning: An overview," in Nonlinear Estimation and Classification, D. D. Denison, M. H. Hansen, C. Holmes, B. Mallick, and B. Yu, Eds. Springer, 2003.
12. S. Mallat and Z. Zhang, "Matching pursuits with time-frequency dictionaries," IEEE Transactions on Signal Processing, vol. 41, no. 12, pp. 3397-3415, 1993.
13. V. Vapnik, Statistical learning theory. Wiley, 1998.
14. T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning. Springer, 2001.
15. F. Girosi and G. Anzellotti, "Convergence rates of approximation by translates," Massachusetts Institute of Technology AI Lab, Tech. Rep. AIM-1288, 1992.
16. B. Schölkopf, R. Herbrich, A. Smola, and R. Williamson, "A generalized representer theorem," NeuroCOLT, Tech. Rep. 81, 2000.
17. A. Rahimi and B. Recht, "Weighted sums of random kitchen sinks: Replacing minimization with randomization in learning," in Advances in Neural Information Processing Systems (NIPS), 2008.
18. P. L. Bartlett and S. Mendelson, "Rademacher and Gaussian complexities: Risk bounds and structural results," Journal of Machine Learning Research (JMLR), vol. 3, pp. 463-482, 2002.
19. N. Aronszajn, "Theory of reproducing kernels," Transactions of the American Mathematical Society, vol. 68, no. 3, pp. 337-404, 1950.
20. F. Cucker and S. Smale, "On the mathematical foundations of learning," Bulletin of the American Mathematical Society, vol. 39, no. 1, pp. 1-49, 2001.
21. W. Rudin, Fourier Analysis on Groups, reprint edition ed., ser. Wiley Classics Library. New York: Wiley-Interscience, 1994.
22. L. Devroye, L. Györfi, and G. Lugosi, A probabilistic theory of pattern recognition. New York: Springer, 1996.
23. C. L. B. D. J. Newman, S. Hettich and C. J. Merz, "UCI repository of machine learning databases," 1998. [Online]. Available: http://www.ics.uci.edu/~mlearn/MLRepository.html
24. M. Ledoux and M. Talagrand, Probability in Banach Spaces: Isoperimetry and Processes. Springer, 1991.