Distributed Statistical Estimation and Rates of Convergence in Normal\n Approximation

2017/04/09 by Stanislav Minsker, Minsker, Stanislav, Nate Strawn +1 · 5 citations
Computer Science · Decision Sciences · Mathematics · #62G35 #68W15 #Advanced Bandit Algorithms Research #Distributed #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Parallel #Statistical Methods and Inference #Statistics Theory (math.ST) #and Cluster Computing (cs.DC)

paper · pdf · doi:10.48550/arxiv.1704.02658

openalex publication_date 2017/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper presents a class of new algorithms for distributed statistical\nestimation that exploit divide-and-conquer approach. We show that one of the\nkey benefits of the divide-and-conquer strategy is robustness, an important\ncharacteristic for large distributed systems. We establish connections between\nperformance of these distributed algorithms and the rates of convergence in\nnormal approximation, and prove non-asymptotic deviations guarantees, as well\nas limit theorems, for the resulting estimators. Our techniques are illustrated\nthrough several examples: in particular, we obtain new results for the\nmedian-of-means estimator, as well as provide performance guarantees for\ndistributed maximum likelihood estimation.\n

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