数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (6): 2198-2216.doi: 10.1007/s10473-021-0624-0
• 论文 • 上一篇
Doualeh ABDILLAHI-ALI, Nourddine AZZAOUI, Arnaud GUILLIN, Guillaume LE MAILLOUX, Tomoko MATSUI
Doualeh ABDILLAHI-ALI, Nourddine AZZAOUI, Arnaud GUILLIN, Guillaume LE MAILLOUX, Tomoko MATSUI
摘要: This paper consider the penalized least squares estimators with convex penalties or regularization norms. We provide sparsity oracle inequalities for the prediction error for a general convex penalty and for the particular cases of Lasso and Group Lasso estimators in a regression setting. The main contribution is that our oracle inequalities are established for the more general case where the observations noise is issued from probability measures that satisfy a weak spectral gap (or Poincaré) inequality instead of Gaussian distributions. We illustrate our results on a heavy tailed example and a sub Gaussian one; we especially give the explicit bounds of the oracle inequalities for these two special examples.
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