Primary Submission Category: Interference and Consistency Violations
Low-rank weighting estimators for causal inference with interference
Authors: Souhardya Sengupta, Kosuke Imai, Georgia Papadogeorgou,
Presenting Author: Souhardya Sengupta*
A primary challenge in observational studies with interference lies in the high dimensionality of the treatment space, arising from the potential for the outcome of a unit to be influenced by treatments applied to other units. In practice, this implies that informative causal inference requires an assumption about the structure of interference patterns. In this paper, we develop a general statistical framework for obtaining causal effect estimators that leverage such a structural assumption. We first show that under an arbitrary interference pattern, the standard inverse probability weighting (IPW) estimator is the only uniformly unbiased weighting estimator. Next, we consider a class of assumptions about interference patterns that can be represented as a low-rank structure of potential outcomes. We then derive an unbiased weighting estimator under such an assumption by minimizing the norm of weights, resulting in a drastic improvement in efficiency over the IPW estimator. When the propensity score is known, the resulting optimal weights are projections of IPW weights onto a subspace that incorporates the low-rank structure. We study the asymptotics of the proposed estimator in the partial interference setting and analyze how misspecifying the low-rank structure affects the proposed estimator, along with a data-driven approach to selecting a low-rank structure among several. Extensive simulations and a real-world application outline the effectiveness of our method.