A new data adaptive elastic net predictive model using hybridized smoothed covariance estimators with information complexity

Abstract

We develop a novel Adaptive Elastic Net (AEN) modelling using a new covariance-regularization approach via the Hybridized Smoothed Covariance Estimators (HSCEs) to identify and select the best subset of predictors in undersized high-dimensional data sets. We introduce and score the Consistent and Misspecification Resistant Information Measure of Complexity $\left(CICOM{P}_{Misspec}\right)$ criterion, and the Extended Consistent Akaike's Information Criterion with Fisher Information $\left(CAIC{F}_E\right)$ in AEN models for the first time. We carry out a large Monte Carlo simulation study using the medianmean-squared-error (MMSE) to demonstrate and compare the performance of the MMSE prediction. This is done using Cross-validated Fit Adaptive Elastic Net (CV-AEN) to avoid double shrinkage by varying both the error variance and the correlation structure of the model. Later, the new proposed AEN model is applied to a real undersized benchmark data set to predict the Riboflavin (Vitamin B2) production to select the best subset of predictors to predict the production rate of vitamin B2 and provide the best predictive model. The proposed new approach enables a simple and reliable identification of the best subset of predictive genes of the production rate of Riboflavin (Vitamin B2) without an exhaustive search of all possible subset selection in undersized high-dimensional data. It is a new and novel approach that has generalizability to other regularized General Linear Regression (GLM) models to determine the best predictor space for undersized data.