Statistical Analysis and Data Mining: The ASA Data Science Journal

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

Early View

Abstract 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

Related Topics

Related Publications

Related Content

Site Footer


This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.