A generalized back-door criterion
This work addresses causal inference challenges in complex graphical models with hidden variables, representing a theoretical extension rather than a practical breakthrough.
The authors generalized Pearl's back-door criterion from directed acyclic graphs (DAGs) to more complex graph types that handle Markov equivalence classes and hidden variables, providing necessary and sufficient graphical criteria for identifying valid adjustment sets and explicit constructions when they exist.
We generalize Pearl's back-door criterion for directed acyclic graphs (DAGs) to more general types of graphs that describe Markov equivalence classes of DAGs and/or allow for arbitrarily many hidden variables. We also give easily checkable necessary and sufficient graphical criteria for the existence of a set of variables that satisfies our generalized back-door criterion, when considering a single intervention and a single outcome variable. Moreover, if such a set exists, we provide an explicit set that fulfills the criterion. We illustrate the results in several examples. R-code is available in the R-package pcalg.