测量数据集的独立性
Measuring Independence of Datasets
摘要：
数据流模型表示这样的设置，其中近似成对或$k$方式的独立性与次线性记忆相当重要。在流模型中，联合分布由$k$元组的流给出，目的是测试在整个流上测量的分量之间的相关性。在流模型中，Indyk和McGregor（SODA 08）最近给出了测量成对独立性的令人兴奋的新结果。Indyk和McGregor方法在流模型中的联合分布和乘积分布之间的统计距离下提供了$\log{n}$ -近似。Indyk和McGregor留下的主要问题是如何改进统计距离度量的$\log n$近似。本文解决了Indyk和McGregor提出的两两独立的统计距离的主要公开问题，并将这一结果推广到任何常数$k$。特别是，我们提出了一种算法，计算$(ε, δ)$ -近似的联合和产品之间的分布定义的流的$k$ -元组的统计距离。我们的算法需要$O(({1\over ε}\log({nm\over δ}))^{(30+k)^k})$内存和一个单一的数据流通过。
英文摘要：
A data stream model represents setting where approximating pairwise, or $k$-wise, independence with sublinear memory is of considerable importance. In the streaming model the joint distribution is given by a stream of $k$-tuples, with the goal of testing correlations among the components measured over the entire stream. In the streaming model, Indyk and McGregor (SODA 08) recently gave exciting new results for measuring pairwise independence. The Indyk and McGregor methods provide $\log{n}$-approximation under statistical distance between the joint and product distributions in the streaming model. Indyk and McGregor leave, as their main open question, the problem of improving their $\log n$-approximation for the statistical distance metric. In this paper we solve the main open problem posed by of Indyk and McGregor for the statistical distance for pairwise independence and extend this result to any constant $k$. In particular, we present an algorithm that computes an $(ε, δ)$-approximation of the statistical distance between the joint and product distributions defined by a stream of $k$-tuples. Our algorithm requires $O(({1\over ε}\log({nm\over δ}))^{(30+k)^k})$ memory and a single pass over the data stream.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
