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.

翻译：我们提出了一种新颖的非参数逐点一致统计检验方法（称为马尔可夫检验器），用于在给定数据集条件下检验有向无环图（DAG）或完全部分有向无环图（CPDAG）模型是否满足马尔可夫条件。同时，我们引入了交叉算法节俭搜索（CAFS）方法，用于拒绝那些未通过马尔可夫检验器测试或不符合边最小化条件的DAG模型。边最小化准则曾被Raskutti和Uhler用作非参数简洁性判据，而CAFS方法可轻松推广至其他简洁性条件。CAFS无需依赖真实图参照，因此可用于从给定数据集中发现能够输出近似真实因果模型的结构学习算法及调参配置。我们为此分析提供了软件工具，该工具适用于处理规模较大或稠密度较高的模型，前提是具备足够快速的逐点条件独立性检验方法。此外，仿真实验表明，CAFS流程能够在未知真实图的情况下筛选出近似正确的模型。