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. 
@article{MM_2011_23_9_a2,
     author = {A. S. Nuzhny},
     title = {Bayesian regularization in the problem of point-by-point function approximation using orthogonalized basis},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {33--42},
     publisher = {mathdoc},
     volume = {23},
     number = {9},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2011_23_9_a2/}
}
TY  - JOUR
AU  - A. S. Nuzhny
TI  - Bayesian regularization in the problem of point-by-point function approximation using orthogonalized basis
JO  - Matematičeskoe modelirovanie
PY  - 2011
SP  - 33
EP  - 42
VL  - 23
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2011_23_9_a2/
LA  - ru
ID  - MM_2011_23_9_a2
ER  - 
%0 Journal Article
%A A. S. Nuzhny
%T Bayesian regularization in the problem of point-by-point function approximation using orthogonalized basis
%J Matematičeskoe modelirovanie
%D 2011
%P 33-42
%V 23
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2011_23_9_a2/
%G ru
%F MM_2011_23_9_a2
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/