Approximation of multidimensional dependency based on an expansion in parametric functions from the dictionary

Abstract

In the present work method for construction of approximation of unknown multidimensional dependency based on data sample is proposed. Approximation is constructed in the class of linear expansions in parametric functions from the dictionary. Parameters of the functions from the dictionary are estimated using gradient methods and expansion coefficients are calculated using adap-tively regularized method of least squares. Regularization is used to increase the stability of iterative estimation of parameters. For additional improvement of stability/generalization ability of approximation specially developed method for boosting is used.