Data adaptive covariate balancing for causal effect estimation for high dimensional data

A key challenge in estimating causal effects from observational data is handling confounding and is commonly achieved through weighting methods that balance distribution of covariates between treatment and control groups. Weighting approaches can be classified by whether weights are estimated using parametric or nonparametric methods, and by whether the model relies on modeling and inverting the propensity score or directly estimates weights to achieve distributional balance by minimizing a measure of dissimilarity between groups. Parametric methods, both for propensity score modeling and direct balancing, are prone to model misspecification. In addition, balancing approaches often suffer from the curse of dimensionality, as they assign equal importance to all covariates, thus potentially de-emphasizing true confounders. Several methods, such as the outcome adaptive lasso, attempt to mitigate this issue through variable selection, but are parametric and focus on propensity score estimation rather than direct balancing. In this paper, we propose a nonparametric direct balancing approach that uses random forests to adaptively emphasize confounders. Our method jointly models treatment and outcome using random forests, allowing the data to identify covariates that influence both processes. We construct a similarity measure, defined by the proportion of trees in which two observations fall into the same leaf node, yielding a distance between treatment and control distributions that is sensitive to relevant covariates and captures the structure of confounding. Under suitable assumptions, we show that the resulting weights converge to normalized inverse propensity scores in the L2 norm and provide consistent treatment effect estimates. We demonstrate the effectiveness of our approach through extensive simulations and an application to a real dataset.