Matching for causal effects via multimarginal optimal transport

Identifying cause and effect is one of the primary goals of scientific research. The leading approaches to uncover causal effects are randomized controlled trials. Unfortunately, such trials are often practically infeasible on ethical grounds, might not be generalizable beyond the experimental setting due to lack of variation in the population, or simply have too few participants to generate robust results due to financial or logistical restrictions. An attractive alternative is to use observational data, which are ubiquitous, often readily available, and comprehensive. The main challenge in using observational data for causal inference is the fact that assignment into treatment is not perfectly randomized. This implies that individuals assigned to different treatments may possess systematically different observable and unobservable covariates. Comparing the outcomes between individuals in different treatment groups may then yield a systematically biased estimator of the true causal effect. Matching methods are designed to balance the treatment samples in such a way that differences between the observed covariates of the groups are minimized. This allows the researcher to directly compare the balanced treatment groups for estimating the true causal effect under the assumption that the unobservable covariates of individuals are similar if their observed covariates are similar.