Learning Directed Acyclic Graphs from Partial Orderings

TL;DR

This paper introduces a framework for learning DAG structures from partial causal orderings, enabling efficient estimation in high-dimensional settings where full orderings are unavailable.

Contribution

It proposes a novel estimation framework and algorithms for DAG learning from partial orderings, bridging the gap between full orderings and unordered data.

Findings

Framework effectively leverages partial orderings for DAG estimation

Algorithms perform well in both low- and high-dimensional scenarios

Numerical studies demonstrate the framework's advantages

Abstract

Directed acyclic graphs (DAGs) are commonly used to model causal relationships among random variables. In general, learning the DAG structure is both computationally and statistically challenging. Moreover, without additional information, the direction of edges may not be estimable from observational data. In contrast, given a complete causal ordering of the variables, the problem can be solved efficiently, even in high dimensions. In this paper, we consider the intermediate problem of learning DAGs when a partial causal ordering of variables is available. We propose a general estimation framework for leveraging the partial ordering and present efficient estimation algorithms for low- and high-dimensional problems. The advantages of the proposed framework are illustrated via numerical studies.