A Topological Sorting Criterion for Random Causal Directed Acyclic Graphs

2026-05-07

AI Summary

This study addresses a critical limitation in the evaluation of causal discovery algorithms, which often rely on randomly generated directed acyclic graphs (DAGs) whose implicit topological properties may distort performance assessments. The authors observe that in common random DAG models—such as Erdős–Rényi and scale-free graphs—the number of “relatives” (nodes reachable via open paths) for each node strictly increases along the true causal order. They prove that this monotonicity property renders the Markov equivalence class degenerate, collapsing it to a single unique graph. Leveraging this insight, they propose a causal ordering recovery criterion based on estimating relative counts and introduce a corresponding time-ordered DAG sampling scheme. Experiments demonstrate that the method efficiently approximates the true causal order across diverse simulation settings, while also exposing inherent limitations in current synthetic data evaluation paradigms.

Abstract

Random directed acyclic graphs (DAGs) based on imposing an order on Erdős-Rényi and scale free random graphs are widely used for evaluating causal discovery algorithms. We show that in such DAGs, the set of nodes reachable via open paths, termed relatives, increases monotonically along the causal order. We assess the prevalence of this pattern numerically, and demonstrate that it can be exploited for causal order recovery via sorting by the estimated number of relatives. We note that many simulations in the literature feature settings where this yields an excellent proxy for the causal order, and show that a strict increase of relatives along the causal order leads to a singular Markov equivalence class. We propose sampling time-series DAGs as a possible alternative and discuss implications for causal discovery algorithms and their evaluation on synthetic data.

Problem

• causal discovery
• directed acyclic graphs
• topological sorting
• Markov equivalence class
• synthetic data

Innovation

• topological sorting
• causal discovery
• directed acyclic graphs
• Markov equivalence class
• relatives monotonicity