Distributed Statistical Estimation and Rates of Convergence in Normal Approximation
Distributed Statistical Estimation and Rates of Convergence in Normal Approximation
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DOI：
10.1214/19-ejs1647
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发表时间：
2017-04
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影响因子：
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通讯作者：
Stanislav Minsker;Nate Strawn
中科院分区：
文献类型：
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作者：
Stanislav Minsker;Nate Strawn
本文介绍了一类新算法，以利用分布和纠纷方法的分布式统计估计。我们表明，分裂和纠纷策略的主要好处之一是鲁棒性，这是大型分布式系统的重要特征。我们在这些分布式算法的性能与正常近似中的收敛速率之间建立了连接，并证明对所得估计器可以保证非反应偏差以及限制定理。通过几个示例来说明我们的技术：特别是，我们获得了均值估计器的新结果，并为分布式最大似然估计提供了性能保证。
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.