\dm_csml_event_details UCL ELLIS

On counterfactual inference with unobserved confounding


Abhin Shah




Friday, 16 June 2023




Function Space, UCL Centre for Artificial Intelligence, 1st Floor, 90 High Holborn, London WC1V 6BH



Event series

DeepMind/ELLIS CSML Seminar Series


Given an observational study with n independent but heterogeneous units, our goal is to learn the counterfactual distribution for each unit using only one p-dimensional sample per unit containing covariates, interventions, and outcomes. Specifically, we allow for unobserved confounding that introduces statistical biases between interventions and outcomes as well as exacerbates the heterogeneity across units. Modeling the underlying joint distribution as an exponential family, we reduce learning the unit-level counterfactual distributions to learning n exponential family distributions with heterogeneous parameters and only one sample per distribution. We introduce a convex objective that pools all n samples to jointly learn all n parameter vectors, and provide a unit-wise mean squared error bound that scales linearly with the metric entropy of the parameter space. For example, when the parameters are s-sparse linear combination of k known vectors, the error is O(s log k/p).  En route, we derive sufficient conditions for compactly supported distributions to satisfy the logarithmic Sobolev inequality. As an application of the framework, our results enable consistent imputation of sparsely missing covariates.


Abhin Shah is a fifth-year Ph.D. student in EECS department at MIT advised by Prof. Devavrat Shah and Prof. Greg Wornell. He is a recipient of MIT’s Jacobs Presidential Fellowship. He interned at Google Research in 2021 and at IBM Research in 2020. Prior to MIT, he graduated from IIT Bombay with a Bachelor’s degree in Electrical Engineering. His research interests include theoretical and applied aspects of trustworthy machine learning with a focus on causality, fairness, and privacy.