分布均匀性测试

O. Fischer, Uri Meir, R. Oshman
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引用次数: 13

摘要

在均匀性测试问题中,我们得到了固定定义域\set1,…上某个未知分布μ的样本。,n,我们的目标是区分μ是均匀分布的情况和μ是ε-在l1距离上不均匀分布的情况。集中式均匀性测试已被广泛研究,已知Θ(√/ε^2)样品是必要和充分的。本文研究了分布均匀性检验:在一个有k个节点的网络中,每个节点i可以从底层分布μ中访问s_i个样本。我们的目标是测试均匀性,同时最小化每个节点的样本数量以及运行时间。我们考虑了几种分布式模型:ŁOCAL模型、CONGEST模型和0轮模型,其中节点完全不能相互通信。我们给出了每个模型的上界,以及0轮模型的下界。我们的结果的关键是分析了在不寻常的误差范围内的集中一致性测试问题,并给出了新的上下界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Distributed Uniformity Testing
In the uniformity testing problem, we are given access to samples from some unknown distribution μ on a fixed domain \set1,..,n , and our goal is to distinguish the case where μ is the uniform distribution from the case where μ is ε-far from uniform in L_1 distance. Centralized uniformity testing has been extensively studied, and it is known that Θ(√ /ε^2) samples are necessary and sufficient. In this paper we study distributed uniformity testing : in a network of k nodes, each node i has access to s_i samples from the underlying distribution μ. Our goal is to test uniformity, while minimizing the number of samples per node, as well as the running time. We consider several distributed models: the ŁOCAL model, the \CONGEST model, and a 0-round model where nodes cannot communicate with each other at all. We give upper bounds for each model, and a lower bound for the 0-round model. The key to our results is analyzing the centralized uniformity-testing problem in an unusual error regime, for which we give new upper and lower bounds.
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