May 7, 2026 · stat.MEJ/K move · Enter open · S save
Alexander G. Reisach, Antoine Chambaz, Gilles Blanchard, Sebastian Weichwald
Laboratoire de Mathématiques d’Orsay Université Paris-Saclay 91400 Orsay, France · CNRS, MAP5 Université Paris Cité F-75006 Paris, France · Department of Mathematical Sciences and Pioneer Centre for Artificial Intelligence, University of Copenhagen, Denmark
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.