Abstract
The role of width in kernel models and radial-basis function networks is investigated with a special emphasis on the Gaussian case. Quantitative bounds are given on kernel-based regularization showing the effect of changing the width. These bounds are shown to be d-th powers of width ratios, and so they are exponential in the dimension of input data.
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References
Fine, T.L.: Feedforward Neural Network Methodology. Springer, Heidelberg (1999)
Kecman, V.: Learning and Soft Computing. MIT Press, Cambridge (2001)
Park, J., Sandberg, I.: Universal approximation using radial–basis–function networks. Neural Computation 3, 246–257 (1991)
Park, J., Sandberg, I.: Approximation and radial basis function networks. Neural Computation 5, 305–316 (1993)
Mhaskar, H.N.: Versatile Gaussian networks. In: Proceedings of IEEE Workshop of Nonlinear Image Processing, pp. 70–73 (1995)
Kainen, P.C., Kůrková, V., Sanguineti, M.: Complexity of Gaussian radial basis networks approximating smooth functions. J. of Complexity 25, 63–74 (2009)
Cucker, F., Smale, S.: On the mathematical foundations of learning. Bulletin of AMS 39, 1–49 (2002)
Poggio, T., Smale, S.: The mathematics of learning: dealing with data. Notices of AMS 50, 537–544 (2003)
Kůrková, V.: Neural network learning as an inverse problem. Logic Journal of IGPL 13, 551–559 (2005)
Gribonval, R., Vandergheynst, P.: On the exponential convergence of matching pursuits in quasi-incoherent dictionaries. IEEE Trans. on Information Theory 52, 255–261 (2006)
Aronszajn, N.: Theory of reproducing kernels. Transactions of AMS 68, 337–404 (1950)
Strichartz, R.: A Guide to Distribution Theory and Fourier Transforms. World Scientific, NJ (2003)
Loustau, S.: Aggregation of SVM classifiers using Sobolev spaces. Journal of Machine Learning Research 9, 1559–1582 (2008)
Girosi, F.: An equivalence between sparse approximation and support vector machines. Neural Computation (AI memo 1606) 10, 1455–1480 (1998)
Girosi, F., Poggio, T.: Regularization algorithms for learning that are equivalent to multilayer networks. Science 247(4945), 978–982 (1990)
Girosi, F., Jones, M., Poggio, T.: Regularization theory and neural networks architectures. Neural Computation 7, 219–269 (1995)
Kůrková, V.: Learning from data as an inverse problem in reproducing kernel Hilbert spaces. Inverse Problems in Science and Engineering (2010) (submitted)
Wahba, G.: Splines Models for Observational Data. SIAM, Philadelphia (1990)
Friedman, A.: Modern Analysis. Dover, New York (1982)
Kůrková, V., Neruda, R.: Uniqueness of functional representations by Gaussian basis function networks. In: Proceedings of ICANN 1994, pp. 471–474. Springer, London (1994)
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Kůrková, V., Kainen, P.C. (2011). Kernel Networks with Fixed and Variable Widths. In: Dobnikar, A., Lotrič, U., Šter, B. (eds) Adaptive and Natural Computing Algorithms. ICANNGA 2011. Lecture Notes in Computer Science, vol 6593. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20282-7_2
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DOI: https://doi.org/10.1007/978-3-642-20282-7_2
Publisher Name: Springer, Berlin, Heidelberg
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