Counting and sampling directed acyclic graphs from a Markov equivalence class are fundamental tasks in graphical causal analysis. In this paper we show that these tasks can be performed in polynomial time, solving a long-standing open problem in this area. Our algorithms are effective and easily implementable. As we show in experiments, these breakthroughs make thought-to-be-infeasible strategies in active learning of causal structures and causal effect identification with regard to a Markov equivalence class practically applicable.

翻译：从马尔可夫等价类中计数和采样有向无环图是图因果分析中的基本任务。本文证明这些任务可在多项式时间内完成，解决了该领域长期存在的公开问题。我们提出的算法高效且易于实现。实验表明，这些突破使原本被认为不可行的因果结构主动学习及基于马尔可夫等价类的因果效应识别策略得以实际应用。