Penerapan Regularisasi Lasso dan Ridge dalam Mengatasi Masalah Multikolinearitas pada Matriks Kovarians

Abstract

The covariance matrix is a relationship measure of how far two or more random variables vary together. In the context of modelling and processing more complex data, the covariance matrix can experience very high multicollinearity and have a determinant value that is very small or even zero so that it becomes singular. This research aims to overcome the problem of singularity in the covariance matrix caused by multicollinearity by applying the L1 (LASSO) regularization penalty which will be compared with the L2 (Ridge) regularization method. Ridge regularization will add a penalty which is then applied to the diagonal value of the covariance matrix so as to reduce the dependency properties and will increase the determinant value of the covariance matrix itself. Meanwhile, LASSO will add a penalty value to the absolute value of all coefficients. The data used is a covariance matrix that is generated with varying dimensions and dependency structures. LASSO method is able to provide a better determinant but lags far enough when compared to the ridge method around 1e˖¹−1e˖⁵and the LASSO method cannot directly maximize the rank value of the matrix. It is very different from the ridge method which is able to maximize the rank value of the covariance matrix that is singular. From these results it can be seen that the ridge method is proven to be better than LASSO in increasing the determinant and rank matrix values of a singular covariance matrix.