  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.
