Adjustment Criteria in Causal Diagrams: An Algorithmic Perspective
This work addresses bias identification in empirical sciences by providing efficient algorithmic tools for causal diagram analysis, representing an incremental advancement over prior methods.
The paper tackled the problem of efficiently identifying and controlling bias in causal diagrams by proving equivalences between adjustment criteria and introducing a simplified notion of d-separation, leading to algorithms that list minimal covariate adjustments with polynomial delay and identify biasing paths in linear time, improving from exponential-time solutions to enable real-time analysis on diagrams with tens to hundreds of variables.
Identifying and controlling bias is a key problem in empirical sciences. Causal diagram theory provides graphical criteria for deciding whether and how causal effects can be identified from observed (nonexperimental) data by covariate adjustment. Here we prove equivalences between existing as well as new criteria for adjustment and we provide a new simplified but still equivalent notion of d-separation. These lead to efficient algorithms for two important tasks in causal diagram analysis: (1) listing minimal covariate adjustments (with polynomial delay); and (2) identifying the subdiagram involved in biasing paths (in linear time). Our results improve upon existing exponential-time solutions for these problems, enabling users to assess the effects of covariate adjustment on diagrams with tens to hundreds of variables interactively in real time.