Estimating Causal Effects Identifiable from a Combination of Observations and Experiments

Learning cause and effect relations is arguably one of the central challenges found throughout the data sciences.Formally, determining whether a collection of observational and interventional distributions can be combined to learn a target causal relation is known as the problem of generalized identification (or g-identification) [Lee et al., 2019]. Although g-identification has been well understood and solved in theory, it turns out to be challenging to apply these results in practice, in particular when considering the estimation of the target distribution from finite samples. In this paper, we develop a new, general estimator that exhibits multiply robustness properties for g-identifiable causal functionals. Specifically, we show that any g-identifiable causal effect can be expressed as a function of generalized multi-outcome sequential back-door adjustments that are amenable to estimation. We then construct a corresponding estimator for the g-identification expression that exhibits robustness properties to bias. We analyze the asymptotic convergence properties of the estimator. Finally, we illustrate the use of the proposed estimator in experimental studies. Simulation results corroborate the theory.