Abstract: This work introduces permutation weighting: a weighting estimator for observational causal inference under general treatment regimes which preserves arbitrary measures of covariate balance. We show that estimating weights which obey balance constraints is equivalent to a simple two-class classification problem between the observed data and a permuted dataset (no matter the cardinality of treatment). Arbitrary probabilistic classifiers may be used in this method; the hypothesis space of the classifier corresponds to the nature of the balance constraints imposed through the resulting weights. We show equivalence between existing covariate balancing weight estimators and permutation weighting and demonstrate estimation with improved efficiency through this regime. We provide theoretical results on the consistency of estimation of causal effects, and the necessity of balance in finite samples. Empirical evaluations indicate that the proposed method outperforms existing state of the art weighting methods for causal effect estimation, even when the data generating process corresponds to the assumptions imposed by prior work.
Drew Dimmery works on the Adaptive Experimentation team at Facebook Core Data Science in New York.