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October 2009 Properties and refinements of the fused lasso
Alessandro Rinaldo
Ann. Statist. 37(5B): 2922-2952 (October 2009). DOI: 10.1214/08-AOS665


We consider estimating an unknown signal, both blocky and sparse, which is corrupted by additive noise. We study three interrelated least squares procedures and their asymptotic properties. The first procedure is the fused lasso, put forward by Friedman et al. [Ann. Appl. Statist. 1 (2007) 302–332], which we modify into a different estimator, called the fused adaptive lasso, with better properties. The other two estimators we discuss solve least squares problems on sieves; one constrains the maximal 1 norm and the maximal total variation seminorm, and the other restricts the number of blocks and the number of nonzero coordinates of the signal. We derive conditions for the recovery of the true block partition and the true sparsity patterns by the fused lasso and the fused adaptive lasso, and we derive convergence rates for the sieve estimators, explicitly in terms of the constraining parameters.


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Alessandro Rinaldo. "Properties and refinements of the fused lasso." Ann. Statist. 37 (5B) 2922 - 2952, October 2009.


Published: October 2009
First available in Project Euclid: 17 July 2009

zbMATH: 1173.62027
MathSciNet: MR2541451
Digital Object Identifier: 10.1214/08-AOS665

Primary: 62G08 , 62G20

Keywords: consistency , Fused lasso , sieve least squares

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 5B • October 2009
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