A sharp oracle inequality for graph-slope

Pierre C. Bellec, Joseph Salmon, Samuel Vaiter

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)4851-4870
Number of pages20
JournalElectronic Journal of Statistics
Issue number2
StatePublished - 2017

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Convex optimization
  • Denoising
  • Graph signal regularization
  • Oracle inequality

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