A Balancing Weight Framework for Estimating the Causal Effect of General Treatments

In observational studies, weighting methods that directly optimize the balance between treatment and covariates have received much attention lately; however these have mainly focused on binary treatments. Inspired by domain adaptation, we show that such methods can be actually reformulated as specific implementations of a discrepancy minimization problem aimed at tackling a shift of distribution from observational to interventional data. More precisely, we introduce a new framework, Covariate Balance via Discrepancy Minimization (CBDM), that provably encompasses most of the existing balancing weight methods and formally extends them to treatments of arbitrary types (e.g., continuous or multivariate). We establish theoretical guarantees for our framework that both offer generalizations of properties known when the treatment is binary, and give a better grasp on what hyperparameters to choose in non-binary settings. Based on such insights, we propose a particular implementation of CBDM for estimating dose-response curves and demonstrate through experiments its competitive performance relative to other existing approaches for continuous treatments.