Causal inference studies whether the presence of a variable influences an
observed outcome. As measured by quantities such as the "average treatment
effect," this paradigm is employed across numerous biological fields, from
vaccine and drug development to policy interventions. Unfortunately, the
majority of these methods are often limited to univariate outcomes. Our work
generalizes causal estimands to outcomes with any number of dimensions or any
measurable space, and formulates traditional causal estimands for nominal
variables as causal discrepancy tests. We propose a simple technique for
adjusting universally consistent conditional independence tests and prove that
these tests are universally consistent causal discrepancy tests. Numerical
experiments illustrate that our method, Causal CDcorr, leads to improvements in
both finite sample validity and power when compared to existing strategies. Our
methods are all open source and available at github.com/ebridge2/cdcorr.

我们的研究将因果估计推广到具有任意个维度或可测空间的结果，将传统的因果估计用于名义变量作为因果差异检验，提出了一种简单的方法来调整普遍一致的条件独立性检验，并证明这些检验是普遍一致的因果差异检验。数值实验证明，我们的方法 Causal CDcorr 与现有策略相比，在有限样本的有效性和功效方面都有所改进。我们的方法都是开源的，可以在 github.com/ebridge2/cdcorr 获取。