CeMMAP Seminar - Anish Agarwal (Columbia)

Abstract: We introduce a framework to formally connect causal inference with matrix/tensor completion. In particular, we represent the various potential outcomes (i.e., counterfactuals) of interest through a matrix/tensor. The key theoretical results presented are: (i) Formal identification results establishing under what missingness patterns, latent confounding, and structure on the matrix/tensor is recovery of unobserved potential outcomes possible. (ii) Introducing novel estimators to recover these unobserved potential outcomes and proving they are finite-sample consistent and asymptotically normal. Through this analysis, we show how to generalize synthetic controls to product counterfactuals under treatment, and how to do entry-wise estimation and inference for matrix completion with missing not at random (MNAR) data. The efficacy of our framework is shown on high-impact applications. These include working with: (i) TaurRx Therapeutics to identify patient sub-populations where their therapy was effective. (ii) Uber Technologies on evaluating the impact of driver engagement policies without running an A/B test. (iii) The Poverty Action Lab at MIT to make personalized policy recommendations to improve childhood immunization rates across villages in Haryana, India.

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