Open Access
2017 A sharp oracle inequality for Graph-Slope
Pierre C. Bellec, Joseph Salmon, Samuel Vaiter
Electron. J. Statist. 11(2): 4851-4870 (2017). DOI: 10.1214/17-EJS1364


Following recent success on the analysis of the Slope estimator, we provide a sharp oracle inequality in term of prediction error for Graph-Slope, a generalization of Slope to signals observed over a graph. In addition to improving upon best results obtained so far for the Total Variation denoiser (also referred to as Graph-Lasso or Generalized Lasso), we propose an efficient algorithm to compute Graph-Slope. The proposed algorithm is obtained by applying the forward-backward method to the dual formulation of the Graph-Slope optimization problem. We also provide experiments showing the practical applicability of the method.


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Pierre C. Bellec. Joseph Salmon. Samuel Vaiter. "A sharp oracle inequality for Graph-Slope." Electron. J. Statist. 11 (2) 4851 - 4870, 2017.


Received: 1 June 2017; Published: 2017
First available in Project Euclid: 30 November 2017

zbMATH: 1382.62014
MathSciNet: MR3732915
Digital Object Identifier: 10.1214/17-EJS1364

Primary: 62G08
Secondary: 62J07

Keywords: Convex optimization , Denoising , graph signal regularization , Oracle inequality

Vol.11 • No. 2 • 2017
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