  Bias in causal comparisons has a direct correspondence with distributional
imbalance of covariates between treatment groups. Weighting strategies such as
inverse propensity score weighting attempt to mitigate bias by either modeling
the treatment assignment mechanism or balancing specified covariate moments.
This paper introduces a new weighting method, called energy balancing, which
instead aims to balance weighted covariate distributions. By directly targeting
distributional imbalance, the proposed weighting strategy can be flexibly
utilized in a wide variety of causal analyses, including the estimation of
average treatment effects and individualized treatment rules. Our energy
balancing weights (EBW) approach has several advantages over existing weighting
techniques. First, it offers a model-free and robust approach for obtaining
covariate balance that does not require tuning parameters, obviating the need
for modeling decisions of secondary nature to the scientific question at hand.
Second, since this approach is based on a genuine measure of distributional
balance, it provides a means for assessing the balance induced by a given set
of weights for a given dataset. Finally, the proposed method is computationally
efficient and has desirable theoretical guarantees under mild conditions. We
demonstrate the effectiveness of this EBW approach in a suite of simulation
experiments, and in studies on the safety of right heart catheterization and
the effect of indwelling arterial catheters.
