Comparison of Methods to Solve Inverse Matrix Problem in Regression

Abstract

The inverse matrix problem in linear regression models is a basic issue for high dimensional data and the reason behind this issue is multicollinearity and identification problem. One of Artificial Intelligence’s (AI) branches, machine learning emphasizes using data and algorithms to replicate the approach by which humans learn, to steadily increase accuracy. One of machine learning’s categories is supervised learning which consists of both predictors and predicted values. The regression model is a supervised learning technique for dealing with continuous data sets. Some existing regression methods are LASSO, generalized inverse, and partial least squares (PLS) regression that is considered as a reference to evaluate the newly proposed methods. Newly proposed methods include ‘Beta Cube’, ‘Compressed Beta Cube’, ‘Compressed LASSO’ and ‘Compressed Generalized inverse’ regression. Two existing data sets ‘NIR (Near-Infrared) Spectra of Biscuit Dough’ and ‘Raman Spectra Analysis of Contents of Polyunsaturated Fatty Acids (PUFA)’ have been considered for comparing the performance of reference and proposed methods. To divide the data into training and testing sets, Monte Carlo Cross Validation has been used, and the root mean square error has been used to evaluate the performance estimation of all techniques. All models are tested through algorithms on the R language.