Permutation Weighting

In observational causal inference, in order to emulate a randomized experiment, weights are used to render treatments independent of observed covariates. This property is known as balance; in its absence, estimated causal effects may be arbitrarily biased. In this work we introduce permutation weighting, a method for estimating balancing weights using a standard binary classifier (regardless of cardinality of treatment). A large class of probabilistic classifiers may be used in this method; the choice of loss for the classifier implies the particular definition of balance. We bound bias and variance in terms of the excess risk of the classifier, show that these disappear asymptotically, and demonstrate that our classification problem directly minimizes imbalance. A wide variety of existing balancing weights may be estimated through this regime, allowing for direct comparison between methods based on classifier loss, as well as hyper-parameter tuning using cross-validation. Empirical evaluations indicate that permutation weighting provides favorable performance in comparison to existing methods.