论文标题
通过嘈杂渠道进行假设测试的隐私 - 效用折衷方案
Privacy-Utility Tradeoff for Hypothesis Testing Over A Noisy Channel
论文作者
论文摘要
我们研究一个假设测试问题，对嘈杂的通道具有隐私限制，并在Neyman-Pearson标准下得出了最佳测试的性能。兴趣的基本限制是II类误差概率指数与信息源的泄漏之间的隐私权权衡权衡（PUT）受到I型错误概率的恒定约束。我们为任何非变化的I型误差概率提供了渐近放置的精确表征。我们的结果意味着，可以容忍更大的I型错误概率无法改善PUT。这样的结果称为强烈的匡威或强烈的定理。为了证明强烈的匡威定理，我们在（Tyagi and Watanabe，2020）中应用了最近提出的技术，并进一步证明了它的通用性。针对多个问题的强烈匡威定理，例如针对嘈杂通道（Sreekumar andGündüz，2020年）对独立性进行的假设检验和具有通信和隐私约束的假设检验（Gilani \ Emph {等人}，2020年），是作为我们的典型案例建立或回收的。
We study a hypothesis testing problem with a privacy constraint over a noisy channel and derive the performance of optimal tests under the Neyman-Pearson criterion. The fundamental limit of interest is the privacy-utility tradeoff (PUT) between the exponent of the type-II error probability and the leakage of the information source subject to a constant constraint on the type-I error probability. We provide an exact characterization of the asymptotic PUT for any non-vanishing type-I error probability. Our result implies that tolerating a larger type-I error probability cannot improve the PUT. Such a result is known as a strong converse or strong impossibility theorem. To prove the strong converse theorem, we apply the recently proposed technique in (Tyagi and Watanabe, 2020) and further demonstrate its generality. The strong converse theorems for several problems, such as hypothesis testing against independence over a noisy channel (Sreekumar and Gündüz, 2020) and hypothesis testing with communication and privacy constraints (Gilani \emph{et al.}, 2020), are established or recovered as special cases of our result.
