Covariate balancing using the integral probability metric for causal
  inference
Insung Kong Yuha Park Joonhyuk Jung Kwonsang Lee Yongdai Kim
Weighting methods in causal inference have been widely used to achieve a
desirable level of covariate balancing. However, the existing weighting methods
have desirable theoretical properties only when a certain model, either the
propensity score or outcome regression model, is correctly specified. In
addition, the corresponding estimators do not behave well for finite samples
due to large variance even when the model is correctly specified. In this
paper, we consider to use the integral probability metric (IPM), which is a
metric between two probability measures, for covariate balancing. Optimal
weights are determined so that weighted empirical distributions for the treated
and control groups have the smallest IPM value for a given set of
discriminators. We prove that the corresponding estimator can be consistent
without correctly specifying any model (neither the propensity score nor the
outcome regression model). In addition, we empirically show that our proposed
method outperforms existing weighting methods with large margins for finite
samples.