Primary Submission Category: Matching, Weighting
Low-rank Covariate Balancing Estimators under Interference
Authors: Souhardya Sengupta, Kosuke Imai, Georgia Papadogeorgou,
Presenting Author: Souhardya Sengupta*
A key methodological challenge in observational studies with interference between units is twofold: (1) each unit’s outcome may depend on many others’ treatments, and (2) treatment assignments may exhibit complex dependencies across units. We develop a general framework for constructing robust causal effect estimators to address these challenges. We first show that, without restricting the patterns of interference, the standard inverse probability weighting (IPW) estimator is the only uniformly unbiased estimator when the propensity score is known. In contrast, no estimator has such a property if the propensity score is unknown. We then introduce a “low-rank structure” of potential outcomes as a broad class of structural assumptions about interference. This framework encompasses common assumptions such as anonymous, nearest-neighbor, and additive interference, while flexibly allowing for more complex study-specific interference assumptions. Under this low-rank assumption, we show how to construct an unbiased weighting estimator for a large class of causal estimands, even when the true propensity score is unknown. If the true propensity score is known, we can obtain an unbiased estimator that is more efficient than the IPW estimator by leveraging a low-rank structure. We establish finite sample and asymptotic properties of the proposed estimators, develop a data-driven procedure to select among candidate low-rank structures, and validate our approach through empirical studies.