Synthetic Potential Outcomes and Causal Mixture Identifiability

A mixture model consists of a latent class that exerts a discrete signal on the observed data. Uncovering these latent classes is fundamental to unsupervised learning. In this paper, we consider the problem of recovering latent classes defined with respect to causal responses. We allow overlapping support in the distributions of these classes, meaning individuals cannot be clustered into groups with a similar response. Instead, we build on a setting from proximal causal inference to develop a method of moments approach to synthetically sample potential outcome distributions. This approach is the first known identifiability result for what we call Mixtures of Treatment Effects (MTEs). More broadly, we show how MTEs fit into a hierarchy of causal identifiability that unifies a number of perspectives on latent class confounding.