  This paper introduces Targeted Function Balancing (TFB), a covariate
balancing weights framework for estimating the average treatment effect of a
binary intervention. TFB first regresses an outcome on covariates, and then
selects weights that balance functions (of the covariates) that are
probabilistically near the resulting regression function. This yields balance
in the regression function's predicted values and the covariates, with the
regression function's estimated variance determining how much balance in the
covariates is sufficient. Notably, TFB demonstrates that intentionally leaving
imbalance in some covariates can increase efficiency without introducing bias,
challenging traditions that warn against imbalance in any variable.
Additionally, TFB is entirely defined by a regression function and its
estimated variance, turning the problem of how best to balance the covariates
into how best to model the outcome. Kernel regularized least squares and the
LASSO are considered as regression estimators. With the former, TFB contributes
to the literature of kernel-based weights. As for the LASSO, TFB uses the
regression function's estimated variance to prioritize balance in certain
dimensions of the covariates, a feature that can be greatly exploited by
choosing a sparse regression estimator. This paper also introduces a balance
diagnostic, Targeted Function Imbalance, that may have useful applications.
