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.

翻译：因果推断研究某个变量的存在是否会影响观测结果。通过“平均处理效应”等量进行度量，这一范式广泛应用于从疫苗药物研发到政策干预等多个生物学领域。然而，大多数方法通常局限于单变量结果。我们的工作将因果估计量推广到任意维度或任意可测空间的结果，并将传统名义变量的因果估计量形式化为因果差异检验。我们提出了一种简单技术来调整普适一致的条件独立性检验，并证明这些检验是普适一致的因果差异检验。数值实验表明，与现有策略相比，我们的方法Causal CDcorr在有限样本有效性和统计功效方面均有提升。所有方法均开源，代码见github.com/ebridge2/cdcorr。