Identification of Conditional Interventional Distributions
This work addresses a foundational problem in causal inference for researchers and practitioners, offering theoretical insights and algorithmic solutions, though it is incremental as it builds on existing do-calculus.
The paper tackles the problem of predicting conditional distributions resulting from interventions in causal models, providing a necessary and sufficient graphical condition for when such distributions can be uniquely computed from causal assumptions and statistical data, and proves the completeness of do-calculus for this identification problem.
The subject of this paper is the elucidation of effects of actions from causal assumptions represented as a directed graph, and statistical knowledge given as a probability distribution. In particular, we are interested in predicting conditional distributions resulting from performing an action on a set of variables and, subsequently, taking measurements of another set. We provide a necessary and sufficient graphical condition for the cases where such distributions can be uniquely computed from the available information, as well as an algorithm which performs this computation whenever the condition holds. Furthermore, we use our results to prove completeness of do-calculus [Pearl, 1995] for the same identification problem.