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

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.本文提出一种适用于基于图形处理器（Graphics Processing Units，GPUs）并行化的高维融合套索回归（Fused Lasso Regression，FLR）问题的主次逼近（Majorization–Minimization，MM）算法。该MM算法稳定且灵活，可在数十次迭代内求解各类设计矩阵与惩罚结构对应的融合套索回归问题。本文同时证明了所提算法的收敛性。通过数值实验将所提算法与现有其他算法进行对比，结果表明，在包括任意设计矩阵下二维融合套索回归在内的诸多场景中，所提MM算法均具有竞争力。此外，本文还展示了GPU并行化的优势。补充材料可在线获取。