Nov

18

2022

When:
Friday, November 18, 2022

11:00 AM - 12:00 PM Central

Where: Online

Audience: Faculty/Staff - Post Docs/Docs - Graduate Students

Contact:
Kisa Kowal
(847) 491-3974

Group: Department of Statistics and Data Science

Category: Academic, Lectures & Meetings

**A modern take on Huber regression**

Po-Ling Loh, Professor in the Statistical Laboratory, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge

Abstract:

In the first part of the talk, we discuss the use of a penalized Huber M-estimator for high-dimensional linear regression. We explain how a fairly straightforward analysis yields high-probability error bounds that hold even when the additive errors are heavy-tailed. However, the parameter governing the shape of the Huber loss must be chosen in relation to the scale of the error distribution. We discuss how to use an adaptive technique, based on Lepski's method, to overcome the difficulties traditionally faced by applying Huber M-estimation in a context where both location and scale are unknown.

In the second part of the talk, we turn to a more complicated setting where both the covariates and responses may be heavy-tailed and/or adversarially contaminated. We show how to modify the Huber regression estimator by first applying an appropriate "filtering" procedure to the data based on the covariates. We prove that in low-dimensional settings, this filtered Huber regression estimator achieves near-optimal error rates. We further show that the commonly used least trimmed squares and least absolute deviation estimators may similarly be made robust to contaminated covariates via the same covariate filtering step. This is based on joint work with Ankit Pensia (UW-Madison) and Varun Jog (Cambridge).