The Selective Regularization of a Linear Regression Model: A Recent Study

Abstract

The construction of a linear regression model incorporating regularisation of the system matrix of normal equations is covered in this article. Only the matrix diagonal entries that correspond to the data with a high correlation are increased, as opposed to the conventional ridge regression, which adds positive parameters to all of a matrix's diagonal terms. This causes the matrix conditioning to decrease, which in turn causes the corresponding regression equation coefficients to decrease. Based on the triangular decomposition of the correlation matrix of the original dataset, selection of the entries to be increased. On a known dataset, the method's efficacy is evaluated using not only ridge regression but also the outcomes of applying the well-known algorithms LARS and Lasso.