Unified Covariate Adjustment for Causal Inference Yonghan Jung 1, and Elias Bareinboim Purdue University

Causal effect identification and estimation are fundamental tasks found throughout the data sciences. Although causal effect identification has been solved in theory, many existing estimators only address a subset of scenarios, known as the sequential back-door adjustment (SBD) (Pearl and Robins, 1995a) or g-formula (Robins, 1986). Recent efforts for developing general-purpose estimators with broader coverage, incorporating the front-door adjustment (FD) (Pearl, 2000) and others, are not scalable due to the high computational cost of summing over a highdimensional set of variables. In this paper, we introduce a novel approach that achieves broad coverage of causal estimands beyond the SBD, incorporating various sum-product functionals like the FD, while achieving scalability - estimated in polynomial time relative to the number of variables and samples in the problem. Specifically, we present the class of unified covariate adjustment (UCA) for which we develop a scalable and doubly robust estimator. In particular, we illustrate the expressiveness of UCA for a wide spectrum of causal estimands (e.g., SBD, FD, and others) in causal inference. We then develop an estimator that exhibits computational efficiency and double robustness. Experiments corroborate the scalability and robustness of the proposed framework.