Ellipsoidal Optimal Recovery: A Minimax Approach to Robust Counterfactual Estimation
Abstract: Consider the problem of quantifying the causal effects of an intervention to determine whether the intervention achieved desired outcomes. Researchers address this problem using statistical, machine learning, or signal processing techniques that have limitations of high bias or need of expert knowledge. We present a new minimax geometric approach called ellipsoidal optimal recovery (EOpR) for estimating the unobservable outcome of a treatment unit. It is an approximation-theoretic technique that recovers unknown observations given a learned signal/principal vector and a set of known observations. The significance of our approach is that it improves pre-treatment fit and mitigates bias of the post-treatment estimate relative to other methods in causal inference. Beyond recovery of the unit of interest, an advantage of EOpR is that it produces worst-case limits over the estimates produced. We assess our approach on synthetically-generated data, on standard datasets commonly used in the econometrics (synthetic control) literature, and in the context of the COVID-19 pandemic, showing better performance than baseline techniques.
Submission Length: Regular submission (no more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=4N67bj9ITs&nesting=2&sort=date-desc
Changes Since Last Submission: Reverted to default template, without modifications in TMLR original format.
Assigned Action Editor: ~Niki_Kilbertus1
Submission Number: 4453
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