Conditional independence (CI) tests are widely used in statistical data analysis, e.g., they are the building block of many algorithms for causal graph discovery. The goal of a CI test is to accept or reject the null hypothesis that $X \perp \!\!\! \perp Y \mid Z$, where $X \in \mathbb{R}, Y \in \mathbb{R}, Z \in \mathbb{R}^d$. In this work, we investigate conditional independence testing under the constraint of differential privacy. We design two private CI testing procedures: one based on the generalized covariance measure of Shah and Peters (2020) and another based on the conditional randomization test of Cand\`es et al. (2016) (under the model-X assumption). We provide theoretical guarantees on the performance of our tests and validate them empirically. These are the first private CI tests that work for the general case when $Z$ is continuous.

翻译：条件独立性检验广泛应用于统计数据分析，例如它是许多因果图发现算法的核心构件。条件独立性检验的目标是接受或拒绝原假设 $X \perp \!\!\! \perp Y \mid Z$，其中 $X \in \mathbb{R}, Y \in \mathbb{R}, Z \in \mathbb{R}^d$。本文研究在差分隐私约束下的条件独立性检验问题。我们设计了两种私密条件独立性检验方法：一种基于Shah和Peters（2020）提出的广义协方差度量，另一种基于Candès等人（2016）提出的条件随机化检验（在模型-X假设下）。我们为提出的检验方法提供了理论性能保证，并通过实验验证了其有效性。这是首个适用于 $Z$ 为连续变量的一般情形的私密条件独立性检验方法。