High-Dimensional Fused Lasso Regression Using Majorization-Minimization and Parallel Processing

• Published in: Journal of computational and graphical statistics Vol. 24; no. 1; pp. 121 - 153
• Main Authors: Yu, Donghyeon, Won, Joong-Ho, Lee, Taehoon, Lim, Johan, Yoon, Sungroh
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 02.01.2015; American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America; Taylor & Francis Ltd
• Subjects: Algorithms; Circuits; Design engineering; Graphics processing unit; Majorization-minimization algorithm; Parallel computation; Parallel processing; Regression Analysis; Studies
• ISSN: 1061-8600; 1537-2715
• DOI: 10.1080/10618600.2013.878662

In this article, we propose a majorization-minimization (MM) algorithm for high-dimensional fused lasso regression (FLR) suitable for parallelization using graphics processing units (GPUs). The MM algorithm is stable and flexible as it can solve the FLR problems with various types of design matrices and penalty structures within a few tens of iterations. We also show that the convergence of the proposed algorithm is guaranteed. We conduct numerical studies to compare our algorithm with other existing algorithms, demonstrating that the proposed MM algorithm is competitive in many settings including the two-dimensional FLR with arbitrary design matrices. The merit of GPU parallelization is also exhibited. Supplementary materials are available online.