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Geoffrey CHINOT (CREST) – "ERM and RERM are tractable and optimal estimators in the ε-contamination model"
Time: 2:00 pm – 3:15 pm
Date: 27 th of May 2019
Place: Room 3001.
Geoffrey CHINOT (CREST) – “ERM and RERM are tractable and optimal estimators in the ε-contamination model”
Abstract: We study the ERM and RERM with Lipschitz and convex loss functions under a subgaussian assumption on the design. We consider a setting where |O| outliers may contaminate the labels. In that case, we show that the error rate is bounded by r(N) + |O|/N, where N is the total number of observations and r(N) is the optimal error rate in the non-contaminated setting. The main result can be used for both non-regularized and regularized procedures. For instance we present results for the Huber’s M-estimators without penalization or regularized by the l1-norm. For these two applications we get minimax-optimal rates in the ε- contamination model.
Cristina BUTUCEA, Alexandre TSYBAKOV, Julie JOSSE, Eric MOULINES, Mathieu ROSENBAUM