Mohamed Ndaoud (ESSEC Business School)
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TITLE / TITRE We consider the high-dimensional linear regression model and assume that a fraction of the responses are contaminated by an adversary with complete knowledge of the data and the underlying distribution. We are interested in the situation when the dense additive noise can be heavy-tailed but the predictors have sub-Gaussian distribution. We establish minimax lower bounds that depend on the fraction of the contaminated data and the tails of the additive noise. Moreover, we design a modification of the square root Slope estimator with several desirable features: (a) it is provably robust to adversarial contamination, with the performance guarantees that take the form of sub-Gaussian deviation inequalities and match the lower error bounds up to log-factors; (b) it is fully adaptive with respect to the unknown sparsity level and the variance of the noise, and (c) it is computationally tractable as a solution of a convex optimization problem. To analyze the performance of the proposed estimator, we prove several properties of matrices with sub-Gaussian rows that could be of independent interest. This is joint work with Stanislav Minsker and Lang Wang. SpeakerMohamed Ndaoud is an Assistant Professor (tenure track) of Statistics at ESSEC Business School, and a member of the Statistics Department of CREST. He received a PhD in theoretical statistics, under the supervision of A.B. Tsybakov. His research interests are in high dimensional statistics. In particular, he is interested in variable selection, community detection and robust statistics in the high dimensional setting. Website: Ìý Ìý |