One hypothetically well‐founded approach for learning a Directed Acyclic Graph (DAG) is to utilize the Markov Chain Monte Carlo (MCMC) techniques. In the MCMC, the uniform noninformative priors on all of the possible graphs are considered. This brings about computational costs, making them impractical for learning the structure of DAGs with numerous variables. In this paper, we focus on the discrete variables and use the data information to restrict the space of possible graphs. This approach can be interpreted as an empirical Bayes paradigm. This means that we use an empirical Bayes approach to make zero prior probability of some possible graphs. For this purpose, we first estimate the potential neighbors using L1‐Regularized Markov Blanket and then determine the candidate causes for each variable by introducing a new criterion. This perspective makes it possible to reduce the search space in the process of the MCMC simulation. The results on the well‐known DAGs show that our method has higher accuracy. The source code is available at http://bs.ipm.ac.ir/softwares/mcmccode.rar.

中文翻译：

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使用MCMC算法学习有向无环图的经验贝叶斯方法

一种有据可查的有向无环图（DAG）学习方法是利用马尔可夫链蒙特卡洛（MCMC）技术。在MCMC中，考虑了所有可能图形上的统一非信息先验。这带来了计算成本，使得它们对于学习具有多个变量的DAG的结构不切实际。在本文中，我们专注于离散变量，并使用数据信息来限制可能图形的空间。这种方法可以解释为经验贝叶斯范式。这意味着我们使用经验贝叶斯方法使某些可能图形的先验概率为零。为此，我们首先使用L1正则化马尔可夫毯子估计潜在的邻居，然后通过引入新的标准确定每个变量的候选原因。这种观点使在MCMC仿真过程中减少搜索空间成为可能。著名DAG的结果表明，我们的方法具有更高的准确性。可从http://bs.ipm.ac.ir/softwares/mcmccode.rar获得源代码。