Modern data analysis frequently relies on the use of large datasets, often
constructed as amalgamations of diverse populations or data-sources.
Heterogeneity across these smaller datasets constitutes two major challenges
for causal inference: (1) the source of each sample can introduce latent
confounding between treatment and effect, and (2) diverse populations may
respond differently to the same treatment, giving rise to heterogeneous
treatment effects (HTEs). The issues of latent confounding and HTEs have been
studied separately but not in conjunction. In particular, previous works only
report the conditional average treatment effect (CATE) among similar
individuals (with respect to the measured covariates). CATEs cannot resolve
mixtures of potential treatment effects driven by latent heterogeneity, which
we call mixtures of treatment effects (MTEs). Inspired by method of moment
approaches to mixture models, we propose "synthetic potential outcomes" (SPOs).
Our new approach deconfounds heterogeneity while also guaranteeing the
identifiability of MTEs. This technique bypasses full recovery of a mixture,
which significantly simplifies its requirements for identifiability. We
demonstrate the efficacy of SPOs on synthetic data.

现代数据分析中常常依赖于使用大型数据集，其中包含多个不同的人群或数据源的综合。这些较小数据集之间的异质性构成了因果推断的两个主要挑战：（1）每个样本的来源可能会引入处理和效果之间的潜在混淆，（2）不同的人群对相同的处理可能会产生不同的反应，导致异质性处理效应。先前的研究只报告了类似个体之间的条件平均处理效应（CATE），而不能解决潜在异质性驱动下的潜在混合处理效应，我们称之为混合处理效应（MTEs）。基于混合模型的时刻方法的启发，我们提出了 “合成潜在结果”（SPOs）的新方法。我们的新方法既可以解决异质性问题，也可以保证 MTE 的可辨识性。这种技术绕过了完全恢复混合模型的要求，极大地简化了其可辨识性的要求。我们在合成数据上展示了 SPOs 的有效性。