Linear-Time Algorithms for Front-Door Adjustment in Causal Graphs

• URL: http://arxiv.org/abs/2211.16468v4
• Date: Fri, 26 Jan 2024 16:03:18 GMT
• Title: Linear-Time Algorithms for Front-Door Adjustment in Causal Graphs
• Authors: Marcel Wien\"obst, Benito van der Zander, Maciej Li\'skiewicz
• Abstract summary: Causal effect estimation from observational data is a fundamental task in empirical sciences. This paper focuses on front-door adjustment -- a classic technique which, using observed mediators, allows to identify causal effects even in the presence of unobserved confounders.
• Score: 3.707290781951909
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Causal effect estimation from observational data is a fundamental task in empirical sciences. It becomes particularly challenging when unobserved confounders are involved in a system. This paper focuses on front-door adjustment -- a classic technique which, using observed mediators allows to identify causal effects even in the presence of unobserved confounding. While the statistical properties of the front-door estimation are quite well understood, its algorithmic aspects remained unexplored for a long time. In 2022, Jeong, Tian, and Bareinboim presented the first polynomial-time algorithm for finding sets satisfying the front-door criterion in a given directed acyclic graph (DAG), with an $O(n^3(n+m))$ run time, where $n$ denotes the number of variables and $m$ the number of edges of the causal graph. In our work, we give the first linear-time, i.e., $O(n+m)$, algorithm for this task, which thus reaches the asymptotically optimal time complexity. This result implies an $O(n(n+m))$ delay enumeration algorithm of all front-door adjustment sets, again improving previous work by a factor of $n^3$. Moreover, we provide the first linear-time algorithm for finding a minimal front-door adjustment set. We offer implementations of our algorithms in multiple programming languages to facilitate practical usage and empirically validate their feasibility, even for large graphs.

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