Abstract:
As is known, the regression analysis task is widely used in machine learning problems, which allows to establish relationship between observed data and compactly store of information. Most often, a regression function is described by a linear combination of some of the selected functions $f_j(X), j = 1, \ldots , m, X \in D \subset R^s$. If the observed data contains a random error, then the regression function restored from the observed data contains a random error and a systematic error depending on the selected functions $f_j$. The article indicates the possibility of optimal selection of functions $f_j$ in the sense of a given functional metric, if it is known that the true dependence is consistent with some functional equation. In some cases (regular grids, $s \leqslant 2$), similar results can be obtained using the random process analysis method. The numerical examples given in this article illustrate much more opportunities for the task of constructing the regression function.