高隐私情形下的互信息隐私约束假设检验
信息论
2017-04-28 v1 math.IT
摘要
假设检验是一种统计推断框架，用于确定给定数据集在一组可能分布中的真实分布。隐私限制可能要求数据管理者或受访者本人在应用随机化隐私机制后才与检验共享数据。本工作将互信息（MI）视为衡量泄露的隐私度量。此外，受 Chernoff-Stein 引理启发，选择（由隐私机制生成的）输出分布对之间的相对熵作为效用度量。对于这些度量，目标是针对二元和 m-元假设检验找到最优隐私-效用权衡（PUT）及相应的最优隐私机制。聚焦于高隐私情形，我们发展了二元和 m-元 PUT 问题的欧几里得信息论近似。这些近似问题的解阐明，基于 MI 的隐私度量以与源符号似然成反比的方式保护其隐私。
引用
@article{arxiv.1704.08347,
title = {Hypothesis Testing under Mutual Information Privacy Constraints in the High Privacy Regime},
author = {Jiachun Liao and Lalitha Sankar and Vincent Y. F. Tan and Flavio P. Calmon},
journal= {arXiv preprint arXiv:1704.08347},
year = {2017}
}
备注
13 pages, 7 figures. The paper is submitted to "Transactions on Information Forensics & Security". Comparing to the paper arXiv:1607.00533 "Hypothesis Testing in the High Privacy Limit", the overlapping content is results for binary hypothesis testing with a zero error exponent, and the extended contents are the results for both m-ary hypothesis testing and binary hypothesis testing with nonzero error exponents