Edinburgh Research Explorer a New Approach for Testing Properties of Discrete Distributions a New Approach for Testing Properties of Discrete Distributions
Edinburgh Research Explorer a New Approach for Testing Properties of Discrete Distributions a New Approach for Testing Properties of Discrete Distributions
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爱丁堡研究探索者测试离散分布属性的新方法测试离散分布属性的新方法
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通讯作者：
D. Kane
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作者：
Ilias Diakonikolas;D. Kane
通过爱丁堡研究探险家访问的出版物的一般权利版权由作者和 /或其他版权所有者保留，这是访问这些出版物的条件，用户认识并遵守与这些权利相关的法律要求。取消政策爱丁堡大学已做出了一切合理的努力，以确保爱丁堡研究Explorer内容符合英国立法。给定样本访问一个或多个未知的离散分布，我们想确定它们是否具有某些全球属性或Epsilon-far，使其具有L1距离（等效，总计变异距离或“统计距离”）在这项工作中，我们提供了一种新的分布测试方法结果，我们解决了各种测试问题的样本复杂性。通过使用标准的L2身份测试仪作为黑盒，我们使用此食谱进行了许多问题。固定分布，（2）两个未知分布之间的紧密测试（具有相等/不等的样本量），（3）独立性测试（在任何数量的维度中），（4）收集的接近度测试分布和（5）对所有这些问题的测试直方图，我们的测试者是最佳的，直到（1）除外，我们的测试者是第一个针对相应问题的样本 - 与先前的结果相比，我们的估计器更简单地陈述和分析。分布。我们的算法的样本复杂性取决于未知分布的结构，而不是它们的域大小，并且与许多自然实例中最糟糕的最佳L1-TESTR相比，我们的技术自然而然地概括了。对于L1距离之外的其他指标，我们将其用作…
General rights Copyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy The University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorer content complies with UK legislation. If you believe that the public display of this file breaches copyright please contact openaccess@ed.ac.uk providing details, and we will remove access to the work immediately and investigate your claim. Abstract—We study problems in distribution property testing: Given sample access to one or more unknown discrete distributions, we want to determine whether they have some global property or are epsilon-far from having the property in L1 distance (equivalently, total variation distance, or " statistical distance "). In this work, we give a novel general approach for distribution testing. We describe two techniques: our first technique gives sample–optimal testers, while our second technique gives matching sample lower bounds. As a consequence, we resolve the sample complexity of a wide variety of testing problems. Our upper bounds are obtained via a modular reduction-based approach. Our approach yields optimal testers for numerous problems by using a standard L2-identity tester as a black-box. Using this recipe, we obtain simple estimators for a wide range of problems, encompassing many problems previously studied in the TCS literature, namely: (1) identity testing to a fixed distribution, (2) closeness testing between two unknown distributions (with equal/unequal sample sizes), (3) independence testing (in any number of dimensions), (4) closeness testing for collections of distributions, and (5) testing histograms. For all of these problems, our testers are sample-optimal, up to constant factors. With the exception of (1), ours are the first sample-optimal testers for the corresponding problems. Moreover, our estimators are significantly simpler to state and analyze compared to previous results. As an important application of our reduction-based technique , we obtain the first adaptive algorithm for testing equivalence between two unknown distributions. The sample complexity of our algorithm depends on the structure of the unknown distributions – as opposed to merely their domain size – and is significantly better compared to the worst-case optimal L1-tester in many natural instances. Moreover, our technique naturally generalizes to other metrics beyond the L1-distance. As an illustration of its flexibility, we use it to …