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General methods have been developed for estimating causal effects from observational data under causal assumptions encoded in the form of a causal graph. Most of this literature assumes that the underlying causal graph is completely specified. However, only observational data is available in most practical settings, which means that one can learn at most a Markov equivalence class (MEC) of the underlying causal graph. In this paper, we study the problem of causal estimation from a MEC represented by a partial ancestral graph (PAG), which is learnable from observational data. We develop a general estimator for any identifiable causal effects in a PAG. The result fills a gap for an end-to-end solution to causal inference from observational data to effects estimation. Specifically, we develop a complete identification algorithm that derives an influence function for any identifiable causal effects from PAGs. We then construct a double/debiased machine learning (DML) estimator that is robust to model misspecification and biases in nuisance function estimation, permitting the use of modern machine learning techniques. Simulation results corroborate with the theory. 

Causal effect identification is one of the most prominent and well-understood problems in causal inference. Despite the generality and power of the results developed so far, there are still challenges in their applicability to practical settings, arguably due to the finitude of the samples. Simply put, there is a gap between causal effect identification and estimation. One popular setting in which sample-efficient estimators from finite samples exist is when the celebrated back-door condition holds. In this paper, we extend weighting-based methods developed for the back-door case to more general settings, and develop novel machinery for estimating causal effects using the weighting-based method as a building block. We derive graphical criteria under which causal effects can be estimated using this new machinery and demonstrate the effectiveness of the proposed method through simulation studies.