Recent years have witnessed growing concerns about the privacy of sensitive
data. In response to these concerns, differential privacy has emerged as a
rigorous framework for privacy protection, gaining widespread recognition in
both academic and industrial circles. While substantial progress has been made
in private data analysis, existing methods often suffer from impracticality or
a significant loss of statistical efficiency. This paper aims to alleviate
these concerns in the context of hypothesis testing by introducing
differentially private permutation tests. The proposed framework extends
classical non-private permutation tests to private settings, maintaining both
finite-sample validity and differential privacy in a rigorous manner. The power
of the proposed test depends on the choice of a test statistic, and we
establish general conditions for consistency and non-asymptotic uniform power.
To demonstrate the utility and practicality of our framework, we focus on
reproducing kernel-based test statistics and introduce differentially private
kernel tests for two-sample and independence testing: dpMMD and dpHSIC. The
proposed kernel tests are straightforward to implement, applicable to various
types of data, and attain minimax optimal power across different privacy
regimes. Our empirical evaluations further highlight their competitive power
under various synthetic and real-world scenarios, emphasizing their practical
value. The code is publicly available to facilitate the implementation of our
framework.

提出了一种差分隐私保护的假设检验方法，扩展了经典的非隐私保护排列检验到隐私保护场景，从而实现有限样本有效性和差分隐私的同时保证。通过引入基于核的测试统计量，提出了两种不同差分隐私保护的核测试方法（dpMMD 和 dpHSIC），具有简单易施行、适用于多种数据类型、在不同隐私保护模式下达到极小 - 最优动力的特点。经实证评估，在各种合成和实际场景下展现出竞争力，突显其实际价值。公开提供的代码有助于我们该方法的实现。