Robust Learning of Mixtures of Gaussians

Date: October 13, 2022
Time: 4:00 pm
Room: DBH 4011
Speaker: Pravesh Kothari 
or a while now, the problem of robustly learning a high-dimensional mixture of Gaussians has had a target on its back. The first works in algorithmic robust statistics found robust algorithms for learning a single Gaussian in 2016. Since then, there has been steady progress including clustering spherical mixtures at statistically optimal separation, clustering non-spherical mixtures, and the related problem of list-decoding mean and covariance in the presence of majority fraction outliers.
In this talk, I will describe our recent resolution to this problem. I will focus on new tools developed in a sequence of works that relate robust clustering to phenomena in high dimensional probability such as anti-concentration and hypercontractivity, their algorithmic counterparts based on the sum-of-squares method and new assumption-free guarantees for the tensor decomposition problem.
Based on joint works with Ainesh Bakshi, Ilias Diakonikolas, Misha Ivkov, He Jia, Daniel Kane, Jacob Steinhardt, David Steurer,

Pravesh K. Kothari is an Assistant Professor of Computer Science at CMU. Highlights of his recent work include a sum-of-squares framework for problems in robust statistics such as learning mixtures of arbitrary Gaussians, optimal spectral algorithms for smoothed constraint satisfaction and applications to extremal combinatorics, and sum-of-squares thresholds for average-case optimization problems such as planted clique and random CSPs. His work has been recognized with an NSF Career Award, a Sloan Faculty Fellowship, and a Google Research Scholar Award.  

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