Abstract
Regularization Algorithm (also called Regularization Network) is a technique for solving problems of learning from examples – in particular, the problem of approximating a multivariate function from sparse data. We analyze behavior of Regularization Algorithm for regularizator parameter equal to zero. We propose an approximative version of algorithm in order to overcome the computational cost for large data sets. We give proof of convergence and estimation for error of approximation.
This paper consists of a part of my Master Thesis supervised by A. Skowron.
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References
Cucker, F., Smale, S.: On the mathematical foundations of learning. Bulletin of AMS 39, 1–49 (2001)
Cucker, F., Smale, S.: Best choices for regularization parameters in learning theory. Foundations of computational Mathematics 2(4), 413–428 (2002)
Dodd, T., Harrison, R.: Iterative Solution to Approximation in Reproducing Kernel Hilbert Spaces. In: 15th IFAC World Congress: b 2002, CDROM (2002)
Evgeniou, T., Pontil, M., Poggio, T.: Regularization Networks and Support Vector Machines. Advances in Computational Mathematics 13, 1–50 (2000)
Friedman, J.H., Hastie, T., Tibshirani, R.: Statistical Learning: Data Mining, Inference, and Prediction. Springer, Heidelberg (2001)
Pal, S.K., Polkowski, L., Skowron, A. (eds.): Rough-Neural Computing: Techniques for Computing with Words, Cognitive Technologies. Springer, Heidelberg (2004)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991)
Poggio, T., Smale, S.: The Mathematics of Learning: dealing with Data. Notices of the AMS 50(5), 537–544 (2003)
Vapnik, V.N.: Statistical Learning Theory. Wiley, New York (1998)
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Jaworski, W. (2004). A Note on the Regularization Algorithm. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds) Rough Sets and Current Trends in Computing. RSCTC 2004. Lecture Notes in Computer Science(), vol 3066. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25929-9_28
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DOI: https://doi.org/10.1007/978-3-540-25929-9_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22117-3
Online ISBN: 978-3-540-25929-9
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