High-dimensional Fused Lasso Regression using Majorization-Minimization and Parallel Processing

TL;DR

This paper introduces a stable, flexible, and GPU-parallelizable majorization-minimization algorithm for high-dimensional fused lasso regression, demonstrating competitive performance and guaranteed convergence.

Contribution

It presents a novel MM algorithm for high-dimensional FLR that is suitable for GPU parallelization and applicable to various design matrices and penalty structures.

Findings

The algorithm converges reliably within few tens of iterations.

It is competitive with existing methods across multiple settings.

GPU parallelization significantly accelerates computations.

Abstract

In this paper, 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.