Identification Methods With Arbitrary Interventional Distributions as Inputs

Causal inference quantifies cause-effect relationships by estimating counterfactual parameters from data. This entails using \emph{identification theory} to establish a link between counterfactual parameters of interest and distributions from which data is available. A line of work characterized non-parametric identification for a wide variety of causal parameters in terms of the \emph{observed data distribution}. More recently, identification results have been extended to settings where experimental data from interventional distributions is also available. In this paper, we use Single World Intervention Graphs and a nested factorization of models associated with mixed graphs to give a very simple view of existing identification theory for experimental data. We use this view to yield general identification algorithms for settings where the input distributions consist of an arbitrary set of observational and experimental distributions, including marginal and conditional distributions. We show that for problems where inputs are interventional marginal distributions of a certain type (ancestral marginals), our algorithm is complete.