Distributed Statistical Estimation and Rates of Convergence in Normal Approximation
This work addresses robustness in large distributed systems for statistical estimation, though it appears incremental with new results for existing methods.
The paper tackles distributed statistical estimation by developing new algorithms based on a divide-and-conquer approach, proving non-asymptotic deviation guarantees and limit theorems for estimators like median-of-means and distributed maximum likelihood.
This paper presents a class of new algorithms for distributed statistical estimation that exploit divide-and-conquer approach. We show that one of the key benefits of the divide-and-conquer strategy is robustness, an important characteristic for large distributed systems. We establish connections between performance of these distributed algorithms and the rates of convergence in normal approximation, and prove non-asymptotic deviations guarantees, as well as limit theorems, for the resulting estimators. Our techniques are illustrated through several examples: in particular, we obtain new results for the median-of-means estimator, as well as provide performance guarantees for distributed maximum likelihood estimation.