Properties and refinements of the fused lasso

By Alessandro Rinaldo. 2008

190 citations recorded by the source corpus.

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 $\ell_1$ 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.

Subfields: Computational Mechanics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/aa0a928ff2d304666f9a4d03586dcbdc3039dc61

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Statistics and Probability

Citations in the corpus

SHRINKAGE ESTIMATION OF REGRESSION MODELS WITH MULTIPLE STRUCTURAL CHANGES (2015, background): “Rinaldo (2009) considers three interrelated least squares procedures for the fused Lasso and study their asymptotic properties in the context of estimating an unknown blocky and sparse signal.”
Univariate mean change point detection: Penalization, CUSUM and optimality (2018, background): “Let u ( λ ) = arg min Let ˆ η k b K k =1 be the collection (cid:0)b b b We thus call ˆ η k b K k =1 the change point estimator induced by u λ , or the change point estimator from the optimization problem (7). b Tibshirani et al. (2005) and Rinaldo (2009).”
SLEP: Sparse Learning with Efficient Projections (2011, background): “Some pr op rties of the fused Lasso have been established in [57].”
Wild binary segmentation for multiple change-point detection (2014, background): “…the context of multiple change-point detection by Rinaldo (2009) [as part of the fused lasso penalty, proposed by P. FRYZLEWICZ Tibshirani et al. (2005) and equivalent to taut string in model (1)] and Rojas and Wahlberg (2014), who also point out that the main result in Rinaldo (2009) is erroneous.”
The Smooth-Lasso and other ℓ1+ℓ2-penalized methods (2011, background): “The results obtained in [27] are established not only under the sparsity assumption, but the model is also supposed to be piecewise constant , that is, the non-zero coeﬃcients are represented in a block shape with equal values inside each block.”
Shrinkage estimation of common breaks in panel data models via adaptive group fused Lasso (2016, unknown): “Let α̃̃ = α̃̃(T̃̃) = (̃1(T̃̃)0 ̃̃+1(T̃̃)0)0 Apparently, the objective function in (2.2) is closely related to the literature on adaptive Lasso (Zou 2006), group Lasso (Yuan and Lin 2006), fused Lasso (Tibshirani et al. 2005 and Rinaldo 2009), and group fused Lasso (Qian and Su 2015).”
An efficient algorithm for a class of fused lasso problems (2010, background): “Some properties of the fused Lasso have been established in [26].”