Practical Algorithms for Orientations of Partially Directed Graphical Models

TL;DR

This paper introduces practical algorithms for orienting undirected edges in partially directed graphs to better infer causal structures from observational data, improving efficiency in causal discovery tasks.

Contribution

It presents two novel, simple, and effective algorithms for the maximal orientation of PDAGs, enhancing existing methods in causal discovery.

Findings

Faster algorithms for maximal orientation of PDAGs.

Improved practical effectiveness in causal discovery.

Enhanced integration with existing causal inference workflows.

Abstract

In observational studies, the true causal model is typically unknown and needs to be estimated from available observational and limited experimental data. In such cases, the learned causal model is commonly represented as a partially directed acyclic graph (PDAG), which contains both directed and undirected edges indicating uncertainty of causal relations between random variables. The main focus of this paper is on the maximal orientation task, which, for a given PDAG, aims to orient the undirected edges maximally such that the resulting graph represents the same Markov equivalent DAGs as the input PDAG. This task is a subroutine used frequently in causal discovery, e. g., as the final step of the celebrated PC algorithm. Utilizing connections to the problem of finding a consistent DAG extension of a PDAG, we derive faster algorithms for computing the maximal orientation by proposing two novel approaches for extending PDAGs, both constructed with an emphasis on simplicity and practical effectiveness.