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arXiv · 1706.06977

A sharp oracle inequality for Graph-Slope

Pierre C Bellec·Joseph Salmon·Samuel Vaiter
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Abstract

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 interest of the method.

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Pierre C Bellec, Joseph Salmon, Samuel Vaiter. 2017-06-21. A sharp oracle inequality for Graph-Slope. https://arxiv.org/abs/1706.06977

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