# A sharp oracle inequality for Graph-Slope

## TL;DR

This paper introduces Graph-Slope, a new estimator for signals on graphs, providing a sharp prediction error bound, an efficient algorithm, and experimental validation, advancing the analysis of graph-based denoising methods.

## Contribution

It presents a sharp oracle inequality for Graph-Slope, improves results over existing Total Variation denoisers, and offers an efficient dual-based algorithm with experimental support.

## Key findings

- Sharp oracle inequality for Graph-Slope prediction error
- Improved performance over Total Variation denoiser
- Efficient dual-based algorithm demonstrated in experiments

## 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.