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Sankhya A

, Volume 79, Issue 2, pp 201–207 | Cite as

Discussion of “concentration for (regularized) empirical risk minimization” by Sara van de Geer and Martin Wainwright

  • Stéphane BoucheronEmail author
Article
  • 67 Downloads

Abstract

Sara van de Geer and Martin Wainwright combine astute convexity arguments and concentration inequalities for suprema of empirical processes to establish generic concentration inequalities for excess penalized risk. This note discusses possible refinements and extensions. In the Gaussian sequence model, concentration of reconstruction error is likely to be improvable and might depend on the effective sparsity of the typical penalized estimator. In the general setting, concentration of excess penalized risk should be complemented by concentration of empirical excess penalized risk. Recent results on penalized least-square estimation pave the way to such a extensions.

Keywords and phrases.

Wilks phenomenon Concentration inequalities Risk estimates Penalization 

AMS (2000) subject classification.

60E15 62G08 62G20 62H30. 

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Copyright information

© Indian Statistical Institute 2017

Authors and Affiliations

  1. 1.LPMA UMR 7599 CNRSUniversité Paris-Diderot (Sorbonne Paris Cités)ParisFrance
  2. 2.DMA UMR 8553 CNRSEcole Normale Supérieure (Paris Sciences et Lettres)ParisFrance

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