  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.
