Topological Sorting Criterion for Random Causal DAGs
A new study demonstrates that in random directed acyclic graphs (DAGs) based on Erdős-Rényi and scale-free models, the set of nodes reachable via open paths—termed relatives—increases monotonically along the causal order. This pattern can be exploited for causal order recovery by sorting nodes by the estimated number of relatives. The authors show that a strict increase of relatives leads to a singular Markov equivalence class, and propose sampling time-series DAGs as an alternative for evaluating causal discovery algorithms. The findings have implications for the design and evaluation of synthetic benchmarks in causal discovery research.
Key facts
- Random DAGs based on Erdős-Rényi and scale-free graphs are widely used for evaluating causal discovery algorithms.
- The set of nodes reachable via open paths (relatives) increases monotonically along the causal order.
- This monotonicity can be exploited for causal order recovery via sorting by estimated number of relatives.
- A strict increase of relatives along the causal order leads to a singular Markov equivalence class.
- Time-series DAGs are proposed as a possible alternative for simulations.
- The study has implications for causal discovery algorithms and their evaluation on synthetic data.
- The paper is available on arXiv under reference 2605.06288.
- The research was submitted to the Statistics > Methodology category.
Entities
Institutions
- arXiv