标题： 高隐私限制下的假设检验 显示英文标题

标题： Hypothesis Testing in the High Privacy Limit

摘要： 在奈曼-皮尔逊形式下的二元假设检验是一种统计推断框架，用于区分由两种不同源分布生成的数据。 隐私限制可能要求数据的管理者或数据响应者自己在向测试方共享数据之前应用一个随机化隐私机制。 使用互信息作为隐私度量，以及输出（后随机化）源类的两个分布之间的相对熵作为效用度量（受切尔诺夫-斯坦因引理的启发），本研究专注于找到一个最优机制，在确保两种源分布的基于互信息的泄漏受到约束的同时，最大化所选效用函数。 聚焦于高隐私区域，提出了对权衡问题的欧几里得信息论（E-IT）近似。 结果表明，E-IT近似解与字母表大小无关，并阐明了基于互信息的隐私度量以相反比例保持源符号的隐私性。 显示英文摘要

摘要： Binary hypothesis testing under the Neyman-Pearson formalism is a statistical inference framework for distinguishing data generated by two different source distributions. Privacy restrictions may require the curator of the data or the data respondents themselves to share data with the test only after applying a randomizing privacy mechanism. Using mutual information as the privacy metric and the relative entropy between the two distributions of the output (postrandomization) source classes as the utility metric (motivated by the Chernoff-Stein Lemma), this work focuses on finding an optimal mechanism that maximizes the chosen utility function while ensuring that the mutual information based leakage for both source distributions is bounded. Focusing on the high privacy regime, an Euclidean information-theoretic (E-IT) approximation to the tradeoff problem is presented. It is shown that the solution to the E-IT approximation is independent of the alphabet size and clarifies that a mutual information based privacy metric preserves the privacy of the source symbols in inverse proportion to their likelihood.