[论文解读] Distributed hypothesis testing under privacy constraints

Sreejith Sreekumar|arXiv (Cornell University)|Sep 1, 2019

Wireless Communication Security Techniques被引用 2

一句话总结

本文研究在隐私约束下的分布式假设检验，其中观察者通过有噪信道将数据传输给具有旁信息的检测器。论文建立了错误指数与隐私之间权衡的单字母内界，特殊情况下给出了精确表征，并分析了在窃听者威胁下的速率、错误指数与安全性之间的权衡。

ABSTRACT

Hypothesis Testing (HT) is one of the central topics of study in statistics. Traditionally, it is assumed that the data on which the hypothesis test is to be performed is available unaltered to the decision maker or detector that performs the hypothesis test. However, this is seldom observed in practice, and often the data is observed remotely, and needs to be communicated to the detector over a noisy communication channel, such as a wired or a wireless communication network. The performance of a hypothesis test obviously depends on how accurately the observed data is communicated to the detector, i.e., less distortion of the data implies better performance. However, in many situations less distortion also implies reduced privacy (security) for the observer as there is the threat of leaking sensitive information to the detector (external eavesdropper). The privacy (security) threat is increasingly becoming an important concern due to the availability of affordable large scale computing resources. In this dissertation, we study HT in a distributed setting, in which the data is observed at a remote node, referred to as observer, and communicated over a noisy channel to the detector, which has access to its own correlated side-information. Considering a hypothesis test on the joint distribution of the observer’s data and detector’s side information, we first study the optimal trade-off between the type I and type II error-exponents, i.e., the trade-off between the asymptotic exponential rate of decay of the type I and type II error probabilities with respect to the number of observed data samples, and establish single-letter inner bounds on this trade-off. Of special interest is the asymmetric case of characterizing the optimal type II error-exponent for a fixed non-zero constraint on the type I error probability, for which we obtain exact single-letter characterization in some special cases. We also investigate the aspects of data privacy in the above setting with a rate-limited noiseless channel by exploring the trade-off between rate, type II error-exponent and privacy. Finally, considering an eavesdropper with access to correlated side-information, we study the trade-off between rate, type II error-exponent and security when the detector and eavesdropper are connected to the observer via a noisy broadcast channel.

研究动机与目标

• 解决在远程观测数据并必须通过有噪信道传输时，同时影响准确性和隐私性的问题。
• 在检测器具有相关旁信息的分布式设置下，建模第一类与第二类错误指数之间的权衡。
• 研究在存在窃听者且其具有相关旁信息的情况下，通信中失真降低对数据隐私的影响。
• 表征在速率受限、无噪信道设置下，通信速率、错误指数与安全性之间的最优平衡。
• 分析有噪广播信道对速率、第二类错误指数与安全性之间权衡的影响，当检测器与窃听者均能访问相关旁信息时。

提出的方法

• 构建一个分布式假设检验框架，其中观察者通过有噪信道向具有相关旁信息的检测器发送数据。
• 利用信息论技术，推导出第一类与第二类错误指数之间权衡的单字母内界。
• 分析固定非零第一类错误概率约束下的非对称情况，在特殊情况下实现精确的单字母表征。
• 提出一种基于窃听者具有相关旁信息时信息泄露的隐私度量。
• 建模从观察者到检测器与窃听者之间的有噪广播信道，研究速率、错误指数与安全性之间的联合权衡。
• 应用率失真理论与隐私漏斗概念，量化在通信约束下安全假设检验的根本极限。

实验结果

研究问题

• RQ1 在具有有噪通信与隐私约束的分布式假设检验中，第一类与第二类错误指数之间的根本权衡是什么？
• RQ2 在特殊情况下，当第一类错误概率被固定为非零值时，如何最大化第二类错误指数？
• RQ3 在使用速率受限的无噪信道时，通信速率、第二类错误指数与隐私之间的最优平衡是什么？
• RQ4 当存在具有相关旁信息的窃听者时，其对速率、错误指数与安全性之间可实现权衡有何影响？
• RQ5 在有噪广播信道设置下，安全假设检验的信息论极限是什么？

主要发现

• 本文在具有有噪信道的分布式假设检验设置下，建立了第一类与第二类错误指数之间权衡的单字母内界。
• 对于具有固定非零第一类错误概率的非对称情况，在特殊情况下推导出最优第二类错误指数的精确单字母表征。
• 在速率受限的无噪信道设置下，量化了速率、第二类错误指数与隐私之间的权衡，表明更高的隐私需要更高的速率或更低的错误指数。
• 当检测器与窃听者通过有噪广播信道连接时，本文表征了速率、第二类错误指数与安全性之间联合权衡的根本极限。
• 结果表明，更高的数据保真度（降低失真）可提升假设检验性能，但会降低隐私，凸显了安全分布式推理中的根本矛盾。
• 该框架揭示，检测器与窃听者处的旁信息相关性显著影响假设检验中可实现的安全性-隐私权衡。