Comparison of Regularized Regression Methods for ~Omics Data

Abstract

Volume 3 • Issue 3 • 1000126 metabolites. Therefore, we considered potato tuber flesh colour as the phenotypic trait of interest, the response in our regression and a large metabolomics data set as the set of predictor variables. For tuber flesh colour, there is a well-established relationship to the carotenoid pathway, and especially to beta caroteen [10], therefore, compounds related to this pathway are expected to be observed in a top list or selected set of predictive variables. We apply a double cross validation scheme to include optimization of any hyperparameters needed in the models and allow estimation of prediction error. We apply different regression methods: ridge regression (RR) [11], LASSO [12], elastic net (EN) [13], principal component regression (PCR) [14], partial least squares regression (PLS) [15], sparse PLS regression (SPLS) [16], support vector regression (SVR) [17] and random forest regression (RF) [18]. We use univariate regression as a reference and compare the results of univariate regressions with multiple regression methods. We also study the properties of these methods both from a theoretical point of view, as well as their performance in practical situations in terms