Practical Algorithms for Orientations of Partially Directed Graphical Models

Malte Luttermann, Marcel Wienöbst, Maciej Liskiewicz

Keywords: Causal graphical models, Directed acyclic graphs, Markov equivalence, Consistent extension, Maximal orientation, Meek rules

TL;DR: We give a practically effective algorithm for the maximal orientation of PDAGs — a task ubiquitous in causal discovery — by exploiting connections to the consistent extension problem, providing efficient new implementations for this task.

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.