Geodesic
Bayesian regularization in the problem of point-by-point function approximation using orthogonalized basis
Matematičeskoe modelirovanie, Tome 23 (2011) no. 9, pp. 33-42.

Voir la notice de l'article provenant de la source Math-Net.Ru

The algorithm of point-by-point approximation of multidimensional scalar function is discussed. The solution is searched as series of basic functions. Regularization of approximation is realized by inclusion of stabilizing functional in the Gaussian form. Regularization parameter is searched using Bayesian method. The proposed algorithm is very inexpensive from a computational point of view. In addition it has a unique analytical solution for regularization parameter in contrast to other Bayesian algorithms.
Keywords: approximation, ill-posed problem, Bayesian regularization, supervised learning. 
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A. S. Nuzhny. Bayesian regularization in the problem of point-by-point function approximation using orthogonalized basis. Matematičeskoe modelirovanie, Tome 23 (2011) no. 9, pp. 33-42. http://geodesic.mathdoc.fr/item/MM_2011_23_9_a2/

[1] A. N. Tikhonov, V. Ya. Arsenin, Metody resheniya nekorrektnykh zadach, Izd. 2-e, Nauka, M., 1979 | MR

[2] D. MacKay, “Bayesian interpolation”, Neural Computation, 4 (1992), 415–447 | DOI

[3] A. S. Nuzhnyi, S. A. Shumskii, “Regulyarizatsiya Baiesa v zadache approksimatsii funktsii mnogikh peremennykh”, Matematicheskoe modelirovanie, 15:9 (2003), 55–63

[4] S. A. Shumskii, Baiesova regulyarizatsiya obucheniya, Materialy shkoly-seminara “Sovremennye problemy neiroinformatiki”, Moskva, 2002 | Zbl

[5] A. P. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelyhood from incomplete data via the EM algorithm”, Journal of the Royal Statistical Society. Ser. B, 39:1 (1977), 1–38 | MR | Zbl

[6] A. Hyvarinen, J. Karhunen, E. Oja, Independent Component analysis, A Wiley-Interscience Publication, 2001

[7] L. D. Landau, E. M. Lifshits, Teoreticheskaya fizika, v. 3, Kvantovaya mekhanika, Nauka, Moskva, 1989 | MR

[8] T. Kohonen, Self-organizing maps, Springer Series in Information Sciences, 30, ed. 3, Springer-Verlag, Berlin, 2001 | DOI | MR | Zbl