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.

翻译：在有向无环图的因果推断中，边的方向通常只能恢复到马尔可夫等价类的程度。本文研究均匀随机有向无环图的马尔可夫等价类。通过塔式分解方法，我们证明当节点数量趋于无穷时，马尔可夫等价类数量与有向无环图数量之比趋近于正常数。对于典型的有向无环图，其马尔可夫等价类中元素的期望数量保持有界。更精确地说，我们证明对于均匀选取的有向无环图，其马尔可夫等价类的规模具有超多项式尾部特征。