2020/06/16 by Atsumori Takahashi, Takahashi, Atsumori, Shunichi Nomura +1
Computer Science · Engineering · Mathematics · #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2006.08965
openalex publication_date 2020/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In high dimensional regression, feature clustering by their effects on outcomes is often as important as feature selection. For that purpose, clustered Lasso and octagonal shrinkage and clustering algorithm for regression (OSCAR) are used to make feature groups automatically by pairwise L1 norm and pairwise L_∞ norm, respectively. This paper proposes efficient path algorithms for clustered Lasso and OSCAR to construct solution paths with respect to their regularization parameters. Despite too many terms in exhaustive pairwise regularization, their computational costs are reduced by using symmetry of those terms. Simple equivalent conditions to check subgradient equations in each feature group are derived by some graph theories. The proposed algorithms are shown to be more efficient than existing algorithms in numerical experiments.