Synthetic Potential Outcomes and Causal Mixture Identifiability

TL;DR

This paper introduces a novel approach to identifying causal heterogeneity in mixture models by using synthetic sampling from counterfactual distributions based on higher-order moments, expanding the understanding of mixture identifiability.

Contribution

It proposes a new grouping criterion based on causal response, distinct from traditional covariate-based clustering, and develops a hierarchy for causal mixture identifiability.

Findings

Introduces synthetic sampling method for causal mixture analysis

Defines a hierarchy of mixture identifiability for causal models

Demonstrates how causal mixtures relate to classical mixture notions

Abstract

Heterogeneous data from multiple populations, sub-groups, or sources is often represented as a ``mixture model'' with a single latent class influencing all of the observed covariates. Heterogeneity can be resolved at multiple levels by grouping populations according to different notions of similarity. This paper proposes grouping with respect to the causal response of an intervention or perturbation on the system. This definition is distinct from previous notions, such as similar covariate values (e.g. clustering) or similar correlations between covariates (e.g. Gaussian mixture models). To solve the problem, we ``synthetically sample'' from a counterfactual distribution using higher-order multi-linear moments of the observable data. To understand how these ``causal mixtures'' fit in with more classical notions, we develop a hierarchy of mixture identifiability.