We study a distributed binary hypothesis testing (HT) problem with communication and security constraints, involving three parties: a remote sensor called Alice, a legitimate decision centre called Bob, and an eavesdropper called Eve, all having their own source observations. In this system, Alice conveys a rate R description of her observation to Bob, and Bob performs a binary hypothesis test on the joint distribution underlying his and Alice's observations. The goal of Alice and Bob is to maximise the exponential decay of Bob's miss-detection (type II-error) probability under two constraints: Bob's false alarm-probability (type-I error) probability has to stay below a given threshold and Eve's uncertainty (equivocation) about Alice's observations should stay above a given security threshold even when Eve learns Alice's message. For the special case of testing against independence, we characterise the largest possible type-II error exponent under the described type-I error probability and security constraints.
Meta-Dependence in Conditional Independence Testing
Thayer School of Engineering Dartmouth College（达特茅斯学院工程学院）；Schmidt Center Broad Institute of MIT and Harvard（MIT和哈佛大学Broad研究所Schmidt中心）；Laboratory for Information and Decision Systems Massachusetts Institute of Technology（信息与决策系统实验室麻省理工学院）；Broad Institute of MIT and Harvard（MIT和哈佛大学Broad研究所）
Distributed Hypothesis Testing based on Unequal-Error Protection Codes
提出了噪声网络上二进制假设检验的编码和检验方案，并推导出相应的第二类误差指数。当通信是在一个离散的无记忆信道（DMC），我们的计划相结合的Shimokawa-Han-Amari的假设检验计划与Borade的不等错误保护（UEP）的信道编码。采用单独的源信道编码架构。所得指数对于新引入的\emph{generalized testing against conditional independence}类是最优的。当通信通过MAC或BC时，我们的方案将混合编码与UEP相结合。由此产生的误差指数在MAC是最佳的情况下，广义测试对条件独立性与独立的观察在两个传感器，当MAC分解成两个单独的DMC。在这种情况下，单独的源-信道编码是足够的;当测试是反对独立性时，在任意相关的传感器观测下，这个相同的结论也成立。对于BC，具有UEP的混合编码的误差指数区域在两个决策中心处获得的指数之间表现出折衷。当两个接收机都以最大化不同假设下的误差指数为目标，并且传感器观测值的边际分布在这些假设下不同时，则可以使用以下策略来减轻这种折衷。传感器的假设，提出了一个试探性的猜测，并适用于我们的编码和测试方案的DMC只为决策中心，是不感兴趣的猜测假设下的指数最大化。
