Recent advances in high dimensional robust statistics

Computer Science/Discrete Mathematics Seminar I
Topic:Recent advances in high dimensional robust statistics
Speaker:Daniel Kane
Affiliation:University of California, San Diego
Date:Monday, December 11
Time/Room:11:00am - 12:15pm/S-101
Video Link:https://video.ias.edu/csdm/2017/1211-DanielKane

It is classically understood how to learn the parameters of a Gaussian even in high dimensions from independent samples. However, estimators like the sample mean are very fragile to noise. In particular, a single corrupted sample can arbitrarily distort the sample mean. More generally we would like to be able to estimate the parameters of a distribution even if a small fraction of the samples are corrupted, potentially adversarially. Classically algorithms for this problem have all fallen into one of two categories: those whose error depends polynomially on the dimension (like the coordinate-wise median), and those whose runtimes are exponential in the dimension (like the Tukey median). We discuss recent work to overcome this barrier, achieving dimension independent error in polynomial time.