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

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 variable...

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Main Authors:	You, Yuan, Lian, Heng, Wang, Lichun
Other Authors:	School of Physical and Mathematical Sciences
Format:	Article
Language:	English
Published:	2013
Subjects:	DRNTU::Science::Mathematics
Online Access:	https://hdl.handle.net/10356/107175 http://hdl.handle.net/10220/17942 http://dx.doi.org/10.1007/s00180-012-0373-6
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Institution:	Nanyang Technological University
Language:	English

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spelling	sg-ntu-dr.10356-1071752019-12-06T22:26:02Z A simple and efficient algorithm for fused lasso signal approximator with convex loss function You, Yuan Lian, Heng Wang, Lichun School of Physical and Mathematical Sciences DRNTU::Science::Mathematics 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. 2013-11-29T06:48:40Z 2019-12-06T22:26:02Z 2013-11-29T06:48:40Z 2019-12-06T22:26:02Z 2013 2013 Journal Article Wang, L., You, Y., & Lian, H. (2013). A simple and efficient algorithm for fused lasso signal approximator with convex loss function. Computational statistics, 28(4), 1699-1714. 1613-9658 https://hdl.handle.net/10356/107175 http://hdl.handle.net/10220/17942 http://dx.doi.org/10.1007/s00180-012-0373-6 en Computational statistics
institution	Nanyang Technological University
building	NTU Library
country	Singapore
collection	DR-NTU
language	English
topic	DRNTU::Science::Mathematics
spellingShingle	DRNTU::Science::Mathematics You, Yuan Lian, Heng Wang, Lichun A simple and efficient algorithm for fused lasso signal approximator with convex loss function
description	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.
author2	School of Physical and Mathematical Sciences
author_facet	School of Physical and Mathematical Sciences You, Yuan Lian, Heng Wang, Lichun
format	Article
author	You, Yuan Lian, Heng Wang, Lichun
author_sort	You, Yuan
title	A simple and efficient algorithm for fused lasso signal approximator with convex loss function
title_short	A simple and efficient algorithm for fused lasso signal approximator with convex loss function
title_full	A simple and efficient algorithm for fused lasso signal approximator with convex loss function
title_fullStr	A simple and efficient algorithm for fused lasso signal approximator with convex loss function
title_full_unstemmed	A simple and efficient algorithm for fused lasso signal approximator with convex loss function
title_sort	simple and efficient algorithm for fused lasso signal approximator with convex loss function
publishDate	2013
url	https://hdl.handle.net/10356/107175 http://hdl.handle.net/10220/17942 http://dx.doi.org/10.1007/s00180-012-0373-6
_version_	1681043019239784448

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

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