A new data adaptive elastic net predictive model using hybridized smoothed covariance estimators with information complexity. Issue 6 (13th April 2019) - Mohebbi, Shima; Pamukcu, Esra; Bozdogan, Hamparsum
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 ( C I C O M P M i s s p e c ) criterion, and the Extended Consistent Akaike's Information Criterion with Fisher Information ( C A I C F E ) in AEN models for the first time. We carry out a large Monte Carlo simulation study using the median mean-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.