A sharp oracle inequality for Graph-Slope
Statistics Theory
2017-11-22 v2 Statistics Theory
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.
Cite
@article{arxiv.1706.06977,
title = {A sharp oracle inequality for Graph-Slope},
author = {Pierre C Bellec and Joseph Salmon and Samuel Vaiter},
journal= {arXiv preprint arXiv:1706.06977},
year = {2017}
}