Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, May 20, 2021, 12:15 pm

**Duration**: 30 minutes

**Location**: Zoom: conference room

**Speaker**: Gleb Novikov

We consider a robust linear regression model y=Xβ+η, where an adversary oblivious to the design matrix X may choose η to be an arbitrary vector with 0 < α < 1 fraction of entries bounded by 1 in absolute value. We show that for Gaussian design matrices the Huber loss estimator for β is consistent for every sample size n= ω(d/α^{2}) and achieves an error rate of O(d/α^{2}n)^{1/2}. Both bounds are optimal (up to constant factors). Prior to our work no estimator was known to be consistent in this model except for quadratic sample size n > d^{2} or for logarithmic inlier fraction α > 1/log n. Our results extend to designs far beyond the Gaussian case and, under some symmetry assumptions on the noise, only require the column span of X to not contain approximately sparse vectors.

This is a joint work with Tommaso d'Orsi and David Steurer.

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