Explore outlier-robust clustering techniques for Gaussian mixtures and non-spherical distributions in this 29-minute IEEE conference talk. Delve into robust statistics, focusing on the main result of robustly clustering Gaussian mixtures and its implications for robust covariance estimation. Examine why mean or covariance separation is insufficient, and learn about TV-separation to parameter separation. Investigate simplifying assumptions, anti-concentration, and an inefficient algorithm before diving into Sum-of-Squares relaxation. Gain insights from speakers representing CMU, UW Madison, Berkeley, UCSD, and UT Austin as they outline proofs and discuss high-level Sum of Squares relaxation techniques.
Outlier-Robust Clustering of Gaussians and Other Non-Spherical Mixtures
Overview
Syllabus
Intro
This paper: Outlier-Robust Clustering Gaussian Mixtures
Robust Statistics
Main result: Robustly clustering Gaussian Mixtures
Consequence of our techniques: Robust Covariance Estimation
Mean or covariance separation does not suffice
Lemma: TV-separation to Parameter separation
Simplifying Assumptions
A Hard Interlude
Anti-Concentration
An Inefficient Algorithm
A Sum-of-Squares Relaxation
High-Level Sum of Squares Relaxation
Proof Outline
Taught by
IEEE FOCS: Foundations of Computer Science
