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.

KEYWORDS:

• Predictive modelling
• adaptive elastic net model
• hybridized smooth covariance estimators
• information complexity

Acknowledgments

Initial working paper version of this paper has been presented as an invited paper at the 8th Conference of Eastern Mediterranean Region (EMR) International Biometric Society (IBS) during 11–15 May 2015 in Cappadocia, Turkey and also at the Department of Statistics at Ankara University, in Ankara, Turkey by Professor Bozdogan. We extend our appreciation to the Scientific Program Committee of EMR-IBS and Ankara University, especially to Professor Olcay Arslan, for her kind invitation to present these new findings. We thank Dr. Kirk Bozdogan of MIT for reading and making comments on an earlier draft of this paper that improved the paper. Furthermore, we also thank Yaojin Sun, doctoral student of Professor Bozdogan for his computational assistance in the Monte Carlo simulation. The authors are grateful to Prof. Ejaz Ahmed for inviting this paper for the Special issue of the Journal of Statistical Computation and Simulation. We also thank the referees for constructive comments that substantially improved the first round of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.