A generalized back-door criterion

TL;DR

This paper extends Pearl's back-door criterion to broader graph classes, providing graphical conditions and explicit sets for causal inference with hidden variables and complex graph structures.

Contribution

It introduces a generalized back-door criterion applicable to more complex graphs, with practical criteria and explicit sets for causal effect identification.

Findings

Provides necessary and sufficient graphical criteria for the generalized back-door criterion.

Offers explicit sets satisfying the criterion when they exist.

Includes illustrative examples and R-code implementation.

Abstract

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.