Causal Tensor Completion

November 24, 2023 11:00 AM Singapore


We introduce a framework to formally connect causal inference with tensor completion. In particular, we represent the various potential outcomes (i.e., counterfactuals) of interest through a tensor. The key theoretical results presented are: (i) Formal identification results establishing under what missingness patterns, latent confounding, and structure on the 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.


  1. “Synthetic Interventions” –
  2. “Causal Matrix Completion” –

About the Speaker

Anish Agarwal joined the Department of Industrial Engineering and Operations Research as an assistant professor in June 2023.

Anish received his PhD from Massachusetts Institute of Technology in 2021 and his MSc (2014) and BSc (2013) from Caltech. For his dissertation, he received the INFORMS George B. Dantzig best thesis award (2nd place), and the ACM SIGMETRICS outstanding thesis award (2nd place). He has also received best paper awards from USINEX NSDI (2023) and the American Statistical Association (2023).

His research interests are in designing and analyzing methods for causal machine learning, and applying it to critical problems in social and engineering systems. Prior to coming to Columbia University, he was a postdoctoral scientist at Amazon, Core AI, and was also a fellow at the Simons Institute, UC Berkeley. He has served as a technical consultant to TauRx Therapeutics and Uber Technologies on questions related to experiment design and causal inference. Prior obtaining his PhD, he was a management consultant at Boston Consulting Group.

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Anish Agarwal (Columbia University) - Causal Tensor Completion