Fast Causal Orientation Learning in Directed Acyclic Graphs

TL;DR

This paper introduces Meek functions and a dynamic programming approach to accelerate causal orientation learning in DAGs, significantly improving efficiency in causal discovery tasks.

Contribution

It presents a novel DP-based method utilizing Meek functions to speed up causal orientation learning and provides bounds and verification techniques for DAG edges.

Findings

The proposed methods outperform previous approaches in runtime.

Meek functions enable efficient application of Meek rules.

The approach includes bounds on oriented edges after intervention.

Abstract

Causal relationships among a set of variables are commonly represented by a directed acyclic graph. The orientations of some edges in the causal DAG can be discovered from observational/interventional data. Further edges can be oriented by iteratively applying so-called Meek rules. Inferring edges' orientations from some previously oriented edges, which we call Causal Orientation Learning (COL), is a common problem in various causal discovery tasks. In these tasks, it is often required to solve multiple COL problems and therefore applying Meek rules could be time-consuming. Motivated by Meek rules, we introduce Meek functions that can be utilized in solving COL problems. In particular, we show that these functions have some desirable properties, enabling us to speed up the process of applying Meek rules. In particular, we propose a dynamic programming (DP) based method to apply Meek functions. Moreover, based on the proposed DP method, we present a lower bound on the number of edges that can be oriented as a result of intervention. We also propose a method to check whether some oriented edges belong to a causal DAG. Experimental results show that the proposed methods can outperform previous work in several causal discovery tasks in terms of running-time.