Split Bregman method for large scale fused Lasso. (English) Zbl 1328.65048

Summary: Ordering 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 the identity matrix. In this paper, we propose an iterative algorithm based on the 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 an 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 comparative genomic hybridization (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, where \(p\) is the number of variables and \(n\) is the number of samples.


65C60 Computational problems in statistics (MSC2010)
62J07 Ridge regression; shrinkage estimators (Lasso)
62H30 Classification and discrimination; cluster analysis (statistical aspects)
62J05 Linear regression; mixed models


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