Robust Statistics, Revisited

Presented on October 31, 2016 at 11:00 a.m. in the Klaus Advanced Computing Building, Room 1116EAnkur Moitra is the Rockwell International Assistant Professor in the Department of Mathematics at MIT and a Principal Investigator in the Computer Science and Artificial Intelligence Lab (CSAIL). The aim of his work is to bridge the gap between theoretical computer science and machine learning by developing algorithms with provable guarantees and foundations for reasoning about their behavior.Runtime: 58:19 minutesStarting from the seminal works of Tukey (1960) and Huber (1962), the field of robust statistics asks: Are there estimators that provable work in the presence of noise? The trouble is that all known provably robust estimators are also hard to compute in high-dimensions. Here, we study a basic problem in robust statistics, posed in various forms in the above works. Given corrupted samples from a high-dimensional Gaussian, are there efficient algorithms to accurately estimate its parameters? We give the first algorithms that are able to tolerate a constant fraction of corruptions that is independent of the dimension. Additionally, we give several more applications of our techniques to product distributions and various mixture models. This is based on joint work with Ilias Diakonikolas, Jerry Li, Gautam Kamath, Daniel Kane and Alistair Stewart