An Equivalence between Sparse Approximation and Support Vector Machines

Neural Computation

Volumn 10, Issue 6, 1998, Pages 1455-1480

  Girosi, Federico ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000249788     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/089976698300017269     Document Type: Article

References (34)

1. Aronszajn, N. (1950). Theory of reproducing kernels. Trans. Amer. Math. Soc., 686, 337-104.
2. Bertero, M. (1986). Regularization methods for linear inverse problems. In C. G. Talenti (Ed.), Inverse problems. Berlin: Springer-Verlag.
3. Boser, B. E., Guyon, I. M., & Vapnik, V. N. (July, 1992). A training algorithm for optimal margin classifier. In Proc. 5th ACM Workshop on Computational Learning Theory (pp. 144-152). Pittsburgh, PA.
4. Breiman, L. (1993). Better subset selection using the non-negative garotte (Tech. Rep.). Berkeley: Department of Statistics, University of California, Berkeley.
5. Chen, S. (1995). Basis pursuit. Unpublished doctoral dissertation, Stanford University.
6. Chen, S., Donoho, D., & Saunders, M. (May, 1995). Atomic decomposition by basis pursuit (Tech. Rep. 479). Stanford, CA: Department of Statistics, Stanford University.
7. Cochran, J. A. (1972). The analysis of linear integral equations. New York: McGrawHill.
8. Coifman, R. R., & Wickerhauser, M. V. (1992). Entropy-based algorithms for best-basis selection. IEEE Transactions on Information Theory, 38, 713-718.
9. Cortes, C., & Vapnik, V. (1995). Support vector networks. Machine Learning, 20, 1-25.
10. Courant, R., & Hilbert, D. (1962). Methods of mathematical physics (Vol. 2). London: Interscience.
11. Daubechies, I. (1992). Ten lectures on wavelets. Philadelphia: SIAM.
12. Girosi, F. (1997). An equivalence between sparse approximation and support vector machines (A.I. Memo No. 1606). Cambridge, MA: MIT Artificial Intelligence Laboratory.
13. Girosi, F., Jones, M., & Poggio, T. (1995). Regularization theory and neural networks architectures. Neural Computation, 7, 219-269.
14. Girosi, F., Poggio, T., & Caprile, B. (1991). Extensions of a theory of networks for approximation and learning: Outliers and negative examples. In R. Lippmann, J. Moody, & D. Touretzky (Eds.), Advances in neural information processings systems 3. San Mateo, CA: Morgan Kaufmann.
15. Harpur, G. F., & Prager, R. W. (1996). Development of low entropy coding in a recurrent network. Network, 7, 277-284.
16. Hochstadt, H. (1973). Integral equations. New York: Wiley.
17. Huber, P. J. (1981). Robust statistics. New York: Wiley.
18. Mallat, S., & Zhang, Z. (1993). Matching pursuit in a time-frequency dictionary. IEEE Transactions on Signal Processing, 41, 3397-3415.
19. Micchelli, C. A. (1986). Interpolation of scattered data: Distance matrices and conditionally positive definite functions. Constructive Approximation, 2, 11-22.
20. Moody, J., & Darken, C. (1989). Fast learning in networks of locally-tuned processing units. Neural Computation, 1(2), 281-294.
21. Morozov, V. A. (1984). Methods for solving incorrectly posed problems. Berlin: Springer-Verlag.
22. Olshausen, B. A., & Field, D. J. (1996). Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature, 381, 607-609.
23. Powell, M. J. D. (1992). The theory of radial basis functions approximation in 1990. In W. A. Light (Ed.), Advances in numerical analysis, Volume 2: Wavelets, subdivision algorithms and radial basis functions (pp. 105-210). New York: Oxford University Press.
24. Schumaker, L. L. (1981). Spline functions: Basic theory. New York: Wiley.
25. Smola, A., & Schölkopf, B. (1998). From regularization operators to support vector kernels. In Advances in neural information processings systems 10. Cambridge, MA: MIT Press.
26. Stewart, J. (1976). Positive definite functions and generalizations, an historical survey. Rocky Mountain J. Math., 6, 409-434.
27. Tibshirani, R. (1994, June). Regression selection and shrinkage via the lasso (Tech. Rep.). Toronto: Department of Statistics, University of Toronto. Available from: ftp://utstat.toronto.edu/pub/tibs/lasso.ps.
28. Tikhonov, A. N., & Arsenin, Y. Y. (1977). Solutions of ill-posed problems. Washington, DC: W. H. Winston.
29. Vapnik, V. N. (1982). Estimation of dependences based on empirical data. Berlin: Springer-Verlag.
30. Vapnik, V. (1995). The nature of statistical learning theory. New York: Springer-Verlag.
31. Vapnik, V., Golowich, S. E., & Smola, A. (1997). Support vector method for function approximation, regression estimation, and signal processing. In M. Mozer, M. Jordan, & T. Petsche (Eds.), Advances in neural information Processings Systems 9 (pp. 281-287). Cambridge, MA: MIT Press.
32. Wahba, G. (1975). Smoothing noisy data by spline functions. Numer. Math, 24, 383-393.
33. Wahba, G. (1990). Splines models for observational data. Philadelphia: SIAM.
34. Yosida, K. (1974). Functional analysis. Berlin: Springer-Verlag.