650757 event 1631707772 1631707772 Title: Robust Learning in High dimension

Date: Thursday, 23 September, 2021
Time: 10:00 am (EST)
Location (Physical): Klaus 2100 (featuring snacks)
Location (Virtual): https://bluejeans.com/851759942/0635  

He Jia
PhD Student
School of Computer Science
Georgia Institute of Technology

Committee:
Santosh Vempala (Advisor) - School of Computer Science, Georgia Institute of Technology
Konstantin Tikhomirov - School of Mathematics, Georgia Institute of Technology
Ashwin Pananjady - School of Industrial & Systems Engineering, Georgia Institute of Technology

Abstract:
Given a collection of observations and a class of models, the objective of a typical unsupervised learning algorithm is to find the model in the class that best fits the data. However, real datasets are typically exposed to some source of noise. Robust statistics focuses on the design of outlier-robust estimators — algorithms that can tolerate a constant fraction of corrupted data points or other small departures from model assumptions, independent of the dimension. In the outlier-robust setting, it is challenging to develop efficient learning algorithms for many well-known high-dimensional models. 

We give an efficient algorithm for the problem of robustly learning Gaussian mixtures. The main tools are an efficient partial clustering algorithm that relies on the sum-of-squares method, and a novel tensor decomposition algorithm that allows errors in both Frobenius norm and low-rank terms. I will also discuss the problems of robustly learning affine transformations and robustly learning multi-view models, and the possible approaches to solve these problems: e.g., robust tensor decomposition.

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