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Distributed Statistical Estimation and Rates of Convergence in Normal Approximation

Banff International Research Station for Mathematical Innovation and Discovery

In this talk, we will present 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 spatial 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. The talk is based on a joint work with Nate Strawn.

Mathematics; Statistics; Numerical analysis

video/mp4

Author affiliation: University of South California

2019-03-20

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68972

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/