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

Narumol  Sudjai; Monthira  Duangsaphon; Chandhanarat  Chandhanayingyong

doi:10.6000/1929-6029.2023.12.13

Authors

Narumol Sudjai Department of Orthopaedic Surgery, Faculty of Medicine Siriraj Hospital, Mahidol University, Bangkok 10700, Thailand https://orcid.org/0009-0008-5016-4827
Monthira Duangsaphon Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120, Thailand
Chandhanarat Chandhanayingyong Department of Orthopaedic Surgery, Faculty of Medicine Siriraj Hospital, Mahidol University, Bangkok 10700, Thailand

DOI:

https://doi.org/10.6000/1929-6029.2023.12.13

Keywords:

High-dimensional sparse data, machine learning, multicollinearity, penalized logistic regression, variable selection method

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.

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