A sharp oracle inequality for Graph-Slope

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 practical applicability of the method.
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Pierre C. Bellec, Joseph Salmon, Samuel Vaiter. A sharp oracle inequality for Graph-Slope. Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2017, 11 (2), pp.4851-4870. ⟨10.1214/17-EJS1364⟩. ⟨hal-01544680⟩

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