Synthetic Interventions

Agarwal, Anish; Shah, Devavrat; Shen, Dennis

Consider a setting where there are $N$ heterogeneous units (e.g., individuals, sub-populations) and $D$ interventions (e.g., socio-economic policies). Our goal is to learn the potential outcome associated with every intervention on every unit (i.e., $N \times D$ causal parameters). Towards this, we present a causal framework, synthetic interventions (SI), to infer these $N \times D$ causal parameters while only observing each of the $N$ units under at most two interventions, independent of $D$. This can be significant as the number of interventions, i.e, level of personalization, grows. Importantly, our estimator also allows for latent confounders that determine how interventions are assigned. Theoretically, under a novel tensor factor model across units, measurements, and interventions, we formally establish an identification result for each of these $N \times D$ causal parameters and establish finite-sample consistency and asymptotic normality of our estimator. The estimator is furnished with a data-driven test to verify its suitability. Empirically, we validate our framework through both experimental and observational case studies; namely, a large-scale A/B test performed on an e-commerce platform, and an evaluation of mobility restriction on morbidity outcomes due to COVID-19. We believe this has important implications for program evaluation and the design of data-efficient RCTs with heterogeneous units and multiple interventions.