Estimating complex causal effects from incomplete observational data

Causal calculus is a tool to express causal effects in the terms of observational probability distributions. The application of causal calculus in the non-parametric form requires only the knowledge of the causal structure. However, some kind of explicit modeling is needed when numeric estimates of the causal effect are to be calculated. In this paper, the estimation of complicated nonlinear causal relationships from observational data is studied. It is demonstrated that the estimation of causal effects does not necessarily require the causal model to be specified parametrically but it suffices to model directly the observational probability distributions. The conditions when this approach produces valid estimates are discussed. Generalized additive models, random forests and neural networks are applied to the estimation of causal effects in examples featuring the backdoor and the frontdoor adjustment.