Split Bregman method for large scale fused Lasso

TL;DR

This paper introduces a split Bregman based iterative algorithm for efficiently solving large-scale fused Lasso problems, outperforming existing methods especially in high-dimensional settings.

Contribution

The paper presents a novel split Bregman algorithm for large-scale fused Lasso, with proven convergence and superior performance on real and artificial data.

Findings

Algorithm is significantly faster than existing solvers.

Effective for large p, small n problems.

Demonstrated on proteomic and genomic data.

Abstract

rdering of regression or classification coefficients occurs in many real-world applications. Fused Lasso exploits this ordering by explicitly regularizing the differences between neighboring coefficients through an $\ell_1$ norm regularizer. However, due to nonseparability and nonsmoothness of the regularization term, solving the fused Lasso problem is computationally demanding. Existing solvers can only deal with problems of small or medium size, or a special case of the fused Lasso problem in which the predictor matrix is identity matrix. In this paper, we propose an iterative algorithm based on split Bregman method to solve a class of large-scale fused Lasso problems, including a generalized fused Lasso and a fused Lasso support vector classifier. We derive our algorithm using augmented Lagrangian method and prove its convergence properties. The performance of our method is tested on both artificial data and real-world applications including proteomic data from mass spectrometry and genomic data from array CGH. We demonstrate that our method is many times faster than the existing solvers, and show that it is especially efficient for large p, small n problems.