The Вayes regularization in the problem of function of many variables approximation

The problem of approximation of multi-dimensional data is a typical inverse problem of the reconstruction of the causes by effects. As the majority of inverse problems, this problem relates to the type of the problems that are poorly determined or ill-posed. A stable solution is reached by the minimization of a regularized learning error. The goal of the regularization is to provide the correctness of the problem by limitation of a variety of admissible solutions. The quality of learning is directly connected with an optimal choice of a regularization. In the present paper we propose a method of an optimal regularization in the approximation problem based on a systematic Bayes approach.