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Activity Number: 16 - Recent Advances and Challenges in High-Dimensional Data Analysis
Type: Topic Contributed
Date/Time: Sunday, July 30, 2017 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #322932 View Presentation
Title: Distributed Statistical Estimation and Rates of Convergence in Normal Approximation
Author(s): Stanislav Minsker*
Companies: University of Southern California
Keywords: Covariance estimation ; Heavy tails ; Matrix completion ; Concentration-of-measure ; principal component analysis ; robust estimation

In this talk, we will present new algorithms for distributed statistical estimation that can take advantage of the divide-and-conquer approach. We show that one of the key benefits attained by an appropriate divide-and-conquer strategy is robustness, an important characteristic of large distributed systems. Moreover, we introduce a class of algorithms that are based on the properties of the geometric median, establish connections between performance of these distributed algorithms and rates of convergence in normal approximation, and provide tight deviations guarantees for resulting estimators in the form of exponential concentration inequalities. Techniques are illustrated with several examples; in particular, we obtain new results for the median-of-means estimator, as well as provide performance guarantees for robust distributed maximum likelihood estimation.

Authors who are presenting talks have a * after their name.

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