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 with rigorous theoretical guarantees that work for the general case when $Z$ is continuous.

翻译：条件独立性（CI）检验广泛应用于统计数据中分析，例如它是因果图发现算法的重要基石。CI检验的目标是接受或拒绝零假设 $X \perp \!\!\! \perp Y \mid Z$，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。我们设计了两种私有CI检验方法：其一基于Shah和Peters（2020）提出的广义协方差度量，其二基于Candès等人（2016）提出的条件随机化检验（在模型-X假设下）。我们为所提出的检验方法提供了理论性能保障，并通过实验验证其有效性。这是首批在$Z$为连续变量的一般情况下具有严格理论保障的私有CI检验方法。