We give a novel nonparametric pointwise consistent statistical test (the Markov Checker) of the Markov condition for directed acyclic graph (DAG) or completed partially directed acyclic graph (CPDAG) models given a dataset. We also introduce the Cross-Algorithm Frugality Search (CAFS) for rejecting DAG models that either do not pass the Markov Checker test or that are not edge minimal. Edge minimality has been used previously by Raskutti and Uhler as a nonparametric simplicity criterion, though CAFS readily generalizes to other simplicity conditions. Reference to the ground truth is not necessary for CAFS, so it is useful for finding causal structure learning algorithms and tuning parameter settings that output causal models that are approximately true from a given data set. We provide a software tool for this analysis that is suitable for even quite large or dense models, provided a suitably fast pointwise consistent test of conditional independence is available. In addition, we show in simulation that the CAFS procedure can pick approximately correct models without knowing the ground truth.

本研究解决了在缺乏真实数据的情况下选择有向无环图 (DAG) 模型的挑战。提出的马尔可夫检验方法与Cross-Algorithm Frugality Search (CAFS)结合，能够有效地拒绝不符合马尔可夫条件或非边最小的DAG模型。关键发现表明，CAFS能在不知道真实标准的情况下，选择出近似正确的模型，具有重要应用潜力。

在缺乏真实数据的情况下，使用马尔可夫和最小边数选择有向无环图模型