A simple and efficient algorithm for fused lasso signal approximator with convex loss function

Authors:
Lichun Wang;Yuan You;Heng Lian
Affiliations:
Department of Mathematics, Beijing Jiaotong University, Beijing, PR China 100044;Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore 637371;Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore 637371
Venue:
Computational Statistics
Year:
2013

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Abstract

We consider the augmented Lagrangian method (ALM) as a solver for the fused lasso signal approximator (FLSA) problem. The ALM is a dual method in which squares of the constraint functions are added as penalties to the Lagrangian. In order to apply this method to FLSA, two types of auxiliary variables are introduced to transform the original unconstrained minimization problem into a linearly constrained minimization problem. Each updating in this iterative algorithm consists of just a simple one-dimensional convex programming problem, with closed form solution in many cases. While the existing literature mostly focused on the quadratic loss function, our algorithm can be easily implemented for general convex loss. We also provide some convergence analysis of the algorithm. Finally, the method is illustrated with some simulation datasets.