Synthetic Interventions
A prototypical example of causal inference with observational data pertains evaluating impact of a policy, such as universal background check for gun purchase, on outcome of interest, such as gun violence, with respect to alternatives such no background check or stricter form of gun control law. Unlike setting of clinical trials where randomized control experiments are feasible, such is not feasibility for policy evaluation. To address this, we present a causal framework, synthetic interventions (SI), that extends synthetic control (SC) to the multiple treatment setting. Formally, given N units (e.g. states) and D interventions (e.g. various gun control policies),the aim of SI is to estimate the counterfactual outcome of each unit under each of the D interventions (including control). We showcase the efficacy of the SI framework on several real-world applications, such as running data-efficient A/B tests in e-commerce and correcting for bias in clinical trials due to dropouts. Finally, we show how to produce tight confidence intervals around our causal estimates. The key to our framework is connection between causal inference and tensor estimation.
Based on joint work with Anish Agarwal and Dennis Shen, both at MIT.
