On the number and size of Markov equivalence classes of random directed acyclic graphs
- In causal inference on directed acyclic graphs, the orientation of edges is in general only recovered up to Markov equivalence classes. We study Markov equivalence classes of uniformly random directed acyclic graphs. Using a tower decomposition, we show that the ratio between the number of Markov equivalence classes and directed acyclic graphs approaches a positive constant when the number of sites goes to infinity. For a typical directed acyclic graph, the expected number of elements in its Markov equivalence class remains bounded. More precisely, we prove that for a uniformly chosen directed acyclic graph, the size of its Markov equivalence class has super-polynomial tails.
| Author: | Dominik SchmidGND, Allan Sly |
|---|---|
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/123074 |
| Parent Title (English): | arXiv |
| Publisher: | arXiv |
| Type: | Preprint |
| Language: | English |
| Date of Publication (online): | 2025/06/25 |
| Year of first Publication: | 2022 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2025/06/26 |
| First Page: | arXiv:2209.04395 |
| DOI: | https://doi.org/10.48550/arXiv.2209.04395 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Stochastik und ihre Anwendungen | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Latest Publications (not yet published in print): | Aktuelle Publikationen (noch nicht gedruckt erschienen) |
