Learning and estimation applications of an online homotopy algorithm for a generalization of the LASSO

Aude Hofleitner; Tarek Rabbani; Mohammad Rafiee; Laurent El Ghaoui; Alex Bayen

doi:10.3934/dcdss.2014.7.503

Article Contents

2014, Volume 7, Issue 3: 503-523. Doi: 10.3934/dcdss.2014.7.503

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Learning and estimation applications of an online homotopy algorithm for a generalization of the LASSO

1.
Electrical Engineering and Computer Science, UC Berkeley
2.
Mechanical Engineering, UC Berkeley
3.
Electrical Engineering and Computer Science, Civil and Environmental Engineering, UC Berkeley

Received: May 2013

Revised: August 2013

Published: June 2014

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Abstract

The LASSO is a widely used shrinkage and selection method for linear regression. We propose a generalization of the LASSO in which the $l_1$ penalty is applied on a linear transformation of the regression parameters, allowing to input prior information on the structure of the problem and to improve interpretability of the results. We also study time varying system with an $l_1$-penalty on the variations of the state, leading to estimates that exhibit few ``jumps''. We propose a homotopy algorithm that updates the solution as additional measurements are available. The algorithm takes advantage of the sparsity of the solution for computational efficiency and is promising for mining large datasets. The algorithm is implemented on three experimental data sets representing applications to traffic estimation from sparsely sampled probe vehicles, flow estimation in tidal channels and text analysis of on-line news.

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Mathematics Subject Classification: Primary: 49M30, 68W27; Secondary: 68U99.

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