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Penalised least square in sparse setting with convex penalty and non gaussian errors

Abstract : This paper considers the penalized least squares estimators with convex penalties or regularisation norms. We provide sparsity oracles 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 contributions are 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, and five easier to verify bounds on compatibility. 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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https://hal.uca.fr/hal-03240201
Contributor : Arnaud Guillin <>
Submitted on : Friday, May 28, 2021 - 8:22:52 AM
Last modification on : Wednesday, June 2, 2021 - 4:27:36 PM

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  • HAL Id : hal-03240201, version 1

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Doualeh Abdillahi-Ali, Nourddine Azzaoui, Arnaud Guillin, Guillaume Le Mailloux, Tomoko Matsui. Penalised least square in sparse setting with convex penalty and non gaussian errors. 2021. ⟨hal-03240201⟩

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