Adaptive Elastic Net on High-Dimensional Sparse Data with Multicollinearity: Application to Lipomatous Tumor Classification

Abstract

Predictive models can experience instabilities because of the combination of high-dimensional sparse data and multicollinearity problems. The adaptive Least Absolute Shrinkage and Selection Operator (adaptive Lasso) and adaptive elastic net were developed using the adaptive weight on penalty term. These adaptive weights are related to the power order of the estimators. Therefore, we concentrate on the power of adaptive weight on these penalty functions. This study purposed to compare the performances of the power of the adaptive Lasso and adaptive elastic net methods under high-dimensional sparse data with multicollinearity. Moreover, we compared the performances of the ridge, Lasso, elastic net, adaptive Lasso, and adaptive elastic net in terms of the mean of the predicted mean squared error (MPMSE) for the simulation study and the classification accuracy for a real-data application. The results of the simulation and the real-data application showed that the square root of the adaptive elastic net performed best on high-dimensional sparse data with multicollinearity.