在缺乏真实标签的情况下使用马尔可夫条件与最小边数选择DAG模型
Choosing DAG Models Using Markov and Minimal Edge Count in the Absence of Ground Truth
AI总结:
本文提出Markov Checker检验和跨算法简约搜索CAFS,在无需真实标签的情况下,通过马尔可夫条件检验和边数最小性准则筛选近似正确的DAG模型,并验证其有效性。
摘要:
我们提出了一种新颖的非参数逐点一致统计检验(Markov Checker),用于在给定数据集的情况下检验有向无环图(DAG)或完全部分有向无环图(CPDAG)模型的马尔可夫条件。我们还引入了跨算法简约搜索(CAFS),用于拒绝那些未通过Markov Checker检验或不是边数最小的DAG模型。边数最小性此前已被Raskutti和Uhler用作非参数简约性准则,不过CAFS可以容易地推广到其他简约性条件。CAFS不需要参考真实标签,因此可用于寻找因果结构学习算法和调节参数设置,使其从给定数据集中输出近似真实的因果模型。我们为该分析提供了一个软件工具,只要具备足够快速的逐点一致条件独立性检验,该工具甚至适用于相当大或稠密的模型。此外,我们在模拟中表明,CAFS过程能够在不知道真实标签的情况下挑选出近似正确的模型。
英文摘要:
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.
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