Adjustment Criteria in Causal Diagrams: An Algorithmic Perspective

TL;DR

This paper introduces efficient algorithms for identifying covariate adjustments and biasing paths in causal diagrams, significantly improving the speed and scalability of causal effect analysis from observational data.

Contribution

It proves equivalences between existing and new adjustment criteria, and provides simplified d-separation notions, enabling polynomial-delay listing and linear-time identification tasks.

Findings

Polynomial delay algorithm for minimal covariate adjustment sets

Linear-time identification of biasing subdiagrams

Improved scalability over exponential-time methods

Abstract

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.