The Annals of Statistics

Properties and refinements of the fused lasso

Alessandro Rinaldo

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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.

Article information

Ann. Statist., Volume 37, Number 5B (2009), 2922-2952.

First available in Project Euclid: 17 July 2009

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Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression 62G20: Asymptotic properties

Fused lasso consistency sieve least squares


Rinaldo, Alessandro. Properties and refinements of the fused lasso. Ann. Statist. 37 (2009), no. 5B, 2922--2952. doi:10.1214/08-AOS665.

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