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UID:1805@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20170612T140000
DTEND;TZID=Europe/Paris:20170612T150000
DTSTAMP:20170528T120000Z
URL:https://www.i2m.univ-amu.fr/evenements/estimation-bounds-and-sharp-ora
 cle-inequalities-of-regularized-procedures-with-lipschitz-loss-functions/
SUMMARY: (...): Estimation bounds and sharp oracle inequalities of regulari
 zed procedures with Lipschitz loss functions
DESCRIPTION:: We obtain estimation error rates and sharp oracle inequalitie
 s for regularization procedures of the formf^∈argminf∈F(1N∑i=1Nℓ(f
 (Xi)\,Yi)+λ∥f∥)when ∥⋅∥ is any norm\, F is a convex class of fu
 nctions and ℓ is a Lipschitz loss function satisfying a Bernstein condit
 ion over F. We explore both the bounded and subgaussian stochastic framewo
 rks for the distribution of the f(Xi)'s\, with no assumption on the distri
 bution of the Yi's. The general results rely on two main objects: a comple
 xity function\, and a sparsity equation\, that depend on the specific sett
 ing in hand (loss ℓ and norm ∥⋅∥).As a proof of concept\, we obtai
 n minimax rates of convergence in the following problems: 1) matrix comple
 tion with any Lipschitz loss function\, including the hinge and logistic l
 oss for the so-called 1-bit matrix completion instance of the problem\, an
 d quantile losses for the general case\, which enables to estimate any qua
 ntile on the entries of the matrix\; 2) logistic LASSO and variants such a
 s the logistic SLOPE\; 3) kernel methods\, where the loss is the hinge los
 s\, and the regularization function is the RKHS norm. http://alquier.ensae
 .net
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DTSTART:20170326T030000
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