In modern data science, it is common that large-scale data are stored and processed parallelly across a great number of locations. For reasons including confidentiality concerns, only limited data information from each parallel center is eligible to be transferred. To solve these problems more efficiently, a group of communication-efficient methods are being actively developed. The first part of our investigation is the distributions of the distributed M-estimators that require a one-step update, combining data information collected from all parallel centers. We reveal that the number of centers plays a critical role. When it is not small compared with the total sample size, a non-negligible impact occurs to the limiting distributions, which turn out to be mixtures involving products of normal random variables. Based on our analysis, we propose a multiplier-bootstrap method for approximating the distributions of these one-step updated estimators.
Our second contribution is that we propose two communication-efficient Newton-type algorithms, combining the M-estimator and the gradient collected from each data center. They are created by constructing two Fisher information estimators globally with those communication-efficient statistics. Enjoying a higher rate of convergence, this framework improves upon existing Newton-like methods. Moreover, we present two bias-adjusted one-step distributed estimators. When the square of the center-wise sample size is of a greater magnitude than the total number of centers, they are as efficient as the global M-estimator asymptotically. The advantages of our methods are illustrated by extensive theoretical and empirical evidences. / Statistics
| Identifer | oai:union.ndltd.org:TEMPLE/oai:scholarshare.temple.edu:20.500.12613/8054 |
| Date | January 2022 |
| Creators | Yin, Ziyan |
| Contributors | Tang, Cheng Yong, Chen, Yong, Dong, Yuexiao, Yang, Wei-shih, 1954- |
| Publisher | Temple University. Libraries |
| Source Sets | Temple University |
| Language | English |
| Detected Language | English |
| Type | Thesis/Dissertation, Text |
| Format | 172 pages |
| Rights | IN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available., http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | http://dx.doi.org/10.34944/dspace/8026, Theses and Dissertations |
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