Journal Article

Properties and Refinements of the Fused Lasso

Rinaldo, Alessandro

2009

Overview

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 ℓ₁ 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.

• Publisher: Institute of Mathematical Statistics,The Institute of Mathematical Statistics
• Subject: 62G08 / 62G20 / Acceleration of convergence / Algebra / Analytical estimating / Asymptotic methods / Asymptotic properties / consistency / Consistent estimators / Coordinate systems / Error rates / Estimating techniques / Estimation bias / Estimators / Exact sciences and technology / Fused lasso / General topics / Least squares / Mathematics / Modeling / Number theory / Numerical analysis / Numerical analysis. Scientific computation / Oracles / Parametric inference / Probability and statistics / Regression analysis / Sciences and techniques of general use / sieve least squares / Statistics / Studies