A Path Algorithm for the Fused Lasso Signal Approximator

• Published in: Journal of computational and graphical statistics Vol. 19; no. 4; pp. 984 - 1006
• Main Author: Hoefling, Holger
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 01.12.2010; JCGS Management Committee of the American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America; Taylor & Francis Ltd
• Subjects: Accuracy; Algorithms; Approximation; Chromosomes; Coefficients; Comparative genomic hybridization; Componentwise operations; Convex optimization; Datasets; Identifiability; Image reconstruction; Lasso; Lasso, LARS, and L₁ Regularization; Mathematical independent variables; Mathematical models; Mathematical problems; Penalized regression; Regression analysis; Studies; Vertices
• ISSN: 1061-8600; 1537-2715
• DOI: 10.1198/jcgs.2010.09208

The Lasso is a very well-known penalized regression model, which adds an L 1 penalty with parameter λ 1 on the coefficients to the squared error loss function. The Fused Lasso extends this model by also putting an L 1 penalty with parameter λ 2 on the difference of neighboring coefficients, assuming there is a natural ordering. In this article, we develop a path algorithm for solving the Fused Lasso Signal Approximator that computes the solutions for all values of λ 1 and λ 2 . We also present an approximate algorithm that has considerable speed advantages for a moderate trade-off in accuracy. In the Online Supplement for this article, we provide proofs and further details for the methods developed in the article.