Generalized Support Vector Regression and Symmetry Functional Regression Approaches to Model the High-Dimensional Data

Abstract

The analysis of the high-dimensional dataset when the number of explanatory variables is greater than the observations using classical regression approaches is not applicable and the results may be misleading. In this research, we proposed to analyze such data by introducing modern and up-to-date techniques such as support vector regression, symmetry functional regression, ridge, and lasso regression methods. In this study, we developed the support vector regression approach called generalized support vector regression to provide more efficient shrinkage estimation and variable selection in high-dimensional datasets. The generalized support vector regression can improve the performance of the support vector regression by employing an accurate algorithm for obtaining the optimum value of the penalty parameter using a cross-validation score, which is an asymptotically unbiased feasible estimator of the risk function. In this regard, using the proposed methods to analyze two real high-dimensional datasets (yeast gene data and riboflavin data) and a simulated dataset, the most efficient model is determined based on three criteria (correlation squared, mean squared error, and mean absolute error percentage deviation) according to the type of datasets. On the basis of the above criteria, the efficiency of the proposed estimators is evaluated.