The selective regularization of a linear regression model

Abstract

This paper discusses constructing a linear regression model with regularization of the system matrix of normal equations. In contrast to the conventional ridge regression, where positive parameters are added to all diagonal terms of a matrix, in the method proposed only those matrix diagonal entries that correspond to the data with a high correlation are increased. This leads to a decrease in the matrix conditioning and, therefore, to a decrease in the corresponding coefficients of the regression equation. The selection of the entries to be increased is based on the triangular decomposition of the correlation matrix of the original dataset. The effectiveness of the method is tested on a known dataset, and it is performed not only with a ridge regression, but also with the results of applying the widespread algorithms LARS and Lasso.