An empirical Bayes approach for learning directed acyclic graph using MCMC algorithm

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.