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DESCRIPTION:\n	\n		\n			\n				TITLE / TITRE\n					Robust and Tuning-Free Sparse Linear Reg
 ression via Square-Root Slope\n					\n					ABSTRACT / RÉSUMÉ \n\n				We consider the hig
 h-dimensional linear regression model and assume that a fraction of the re
 sponses are contaminated by an adversary with complete knowledge of the da
 ta and the underlying distribution. We are interested in the situation whe
 n the dense additive noise can be heavy-tailed but the predictors have sub
 -Gaussian distribution. We establish minimax lower bounds that depend on t
 he fraction of the contaminated data and the tails of the additive noise. 
 Moreover\, we design a modification of the square root Slope estimator wit
 h several desirable features: (a) it is provably robust to adversarial con
 tamination\, with the performance guarantees that take the form of sub-Gau
 ssian deviation inequalities and match the lower error bounds up to log-fa
 ctors\; (b) it is fully adaptive with respect to the unknown sparsity leve
 l 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 wor
 k with Stanislav Minsker and Lang Wang.\n\n				\n					Speaker\n				\n\n				Mohamed Ndaoud i
 s an Assistant Professor (tenure track) of Statistics at ESSEC Business Sc
 hool\, and a member of the Statistics Department of CREST. He received a P
 hD 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 stat
 istics in the high dimensional setting.\n\n				Website: https://sites.google.c
 om/view/mndaoud/home\n\n				 \n\n				 \n			\n		\n	\n\n
DTSTART:20231117T203000Z
DTEND:20231117T213000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Mohamed Ndaoud (ESSEC Business School)
URL:/mathstat/channels/event/mohamed-ndaoud-essec-busi
 ness-school-352701
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