Primary Submission Category: Heterogeneous Treatment Effects
Synthetic Combinations: A Causal Inference Framework for Combinatorial Interventions
Authors: Abhineet Agarwal, Anish Agarwal, Suhas Vijaykumar,
Presenting Author: Abhineet Agarwal*
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 x 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 (e.g., multivariate tests on digital platforms), combination therapies in medicine, rankings in recommendation engines, etc. Running N x 2^p experiments to estimate all parameters is likely infeasible as N and p grow. Further, with observational data there is likely confounding. To address these challenges, we propose a novel latent factor model that imposes structure across units (i.e., the matrix of potential outcomes is rank r) and combinations of interventions (i.e., Fourier expansion of the potential outcomes is s sparse). We establish identification for all N x 2^p parameters despite unobserved confounding. We propose an estimation procedure, Synthetic Combinations, and establish it is finite-sample consistent and asymptotically normal. Synthetic Combinations is consistent given poly(r) x (N + s^2p) observations, while previous methods have sample scaling as min(N x s^2p, poly(r) x (N + 2^p)). We also use Synthetic Combinations to propose a data-efficient experimental design mechanism. Empirically, we show Synthetic Combinations outperforms competing approaches on a real-world dataset on movie recommendations.