Causal Mixture Models: Characterization and Discovery
Sarah Mameche, Janis Kalofolias, Jilles Vreeken
Real-world datasets are often comprised of combinations of unobserved subpopulations with distinct underlying causal processes. In an observational study, for example, patients may fall into unobserved groups that either (a) respond effectively to a drug vs. (b) show no response due to drug resistance. If we do not account for this, we will obtain biased estimates of drug effectiveness. In this work, we formulate such settings as a causal mixture model, where the data-generating process of each variable depends on membership to a certain group (a or b). Specifically, we assume a mixture of structural causal equation models with latent categorical variables indexing subpopulation assignment. Unlike prior work, our framework allows for multiple such latent variables affecting distinct observed variable sets. To infer this model from mixed data sources, we propose a topological ordering-based approach that jointly discovers (i) the causal graph and (ii) the number of mixing variables, number of their components, and assignments. In empirical evaluations, we show that our approach effectively discovers these in practice and that mixed data sources can even enhance the identification of cause-effect relationships.