Identification Methods With Arbitrary Interventional Distributions as Inputs
This work provides a more flexible framework for causal inference, potentially benefiting researchers and practitioners in fields like epidemiology and social sciences, though it appears incremental as it builds on existing identification theory.
The paper tackles the problem of causal inference by developing general identification algorithms that can handle arbitrary sets of observational and experimental distributions as inputs, including marginal and conditional distributions, and proves completeness for specific types of interventional marginal distributions.
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.