Synthetic Combinations: A Causal Inference Framework for Combinatorial Interventions

We consider a setting where there are N heterogeneous units and p interventions. Our goal is to learn unit-specific potential outcomes for any combination of these p interventions, i.e., N \times 2 p causal parameters. Choosing a combination of interventions is a problem that naturally arises in a variety of applications such as factorial design experiments and recommendation engines (e.g., showing a set of movies that maximizes engagement for a given user). Running N \times 2 p experiments to estimate the various parameters is likely expensive and/or infeasible as N and p grow. Further, with observational data there is likely confounding, i.e., whether or not a unit is seen under a combination is correlated with its potential outcome under that combination. We study this problem under a novel model that imposes latent structure across both units and combinations of interventions.