Relaxed Adaptive Lasso for Classification on High-Dimensional Sparse Data with Multicollinearity

Abstract

High-dimensional sparse data with multicollinearity is frequently found in medical data. This problem can lead to poor predictive accuracy when applied to a new data set. The Least Absolute Shrinkage and Selection Operator (Lasso) is a popular machine-learning algorithm for variable selection and parameter estimation. Additionally, the adaptive Lasso method was developed using the adaptive weight on the l1-norm penalty. This adaptive weight is related to the power order of the estimators. Thus, we focus on 1) the power of adaptive weight on the penalty function, and 2) the two-stage variable selection method. This study aimed to propose the relaxed adaptive Lasso sparse logistic regression. Moreover, we compared the performances of the different penalty functions by using the mean of the predicted mean squared error (MPMSE) for the simulation study and the accuracy of classification for a real-data application. The results showed that the proposed method performed best on high-dimensional sparse data with multicollinearity. Along with, for classifier with the support vector machine, this proposed method was also the best option for the variable selection process.