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

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, May 02, 2023, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Gleb Novikov

Robust Mean Estimation Without a Mean: Dimension-Independent Error in Polynomial Time for Symmetric Distributions

We study the problem of robustly estimating the mean/location parameter of distributions without moment bounds. We focus on large classes of distributions extensively studied in statistics: symmetric product distributions and elliptical distributions. Concretely, suppose an adversary can arbitrarily corrupt an $\varepsilon$-fraction of the observed d-dimensional samples. For every natural number k, we design an estimator that, using \tilde{O}(d^k) samples, achieves error O(\varespsilon^{1−1/(2k)}). This estimator can be computed in polynomial time. Previously, such results where only known for distributions that have 2k moments that are \emph{certifiably bounded} in sum-of-squares. For the class of distributions we consider, all previous estimators either require exponential time or incur error depending on the dimension. Our algorithms are based on a generalization of the filtering technique [DK22]. We show how this machinery can be combined with Huber-loss-based approach to work with projections of the noise onto some balls. These projections have nice behaviour, and it allows us to use sum-of-squares proofs to obtain algorithmic guarantees even for distributions without first moment. We believe that this approach may find other application in future works.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login