2023/06/25 by Meixia Lin, Lin, Meixia, Yancheng Yuan +5 · 2 citations
Biochemistry, Genetics and Molecular Biology · Immunology and Microbiology · Mathematics · #Cancer, Lipids, and Metabolism #FOS: Mathematics #Optimization and Control (math.OC) #Statistical Methods and Inference #interferon and immune responses
paper · pdf · doi:10.48550/arxiv.2306.14196
openalex publication_date 2023/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The exclusive lasso (also known as elitist lasso) regularizer has become popular recently due to its superior performance on intra-group feature selection. Its complex nature poses difficulties for the computation of high-dimensional machine learning models involving such a regularizer. In this paper, we propose a highly efficient dual Newton method based proximal point algorithm (PPDNA) for solving large-scale exclusive lasso models. As important ingredients, we systematically study the proximal mapping of the weighted exclusive lasso regularizer and the corresponding generalized Jacobian. These results also make popular first-order algorithms for solving exclusive lasso models more practical. Extensive numerical results are presented to demonstrate the superior performance of the PPDNA against other popular numerical algorithms for solving the exclusive lasso problems.