Learning directed acyclic graphs by determination of candidate causes for discrete variables

ABSTRACT

The aim of this paper is learning directed acyclic graph (DAG) by determination of candidate causes for each discrete variable. Based on the fact that the candidate causes of a variable must be a subset of its potential neighbours, we first estimate the potential neighbours for each variable using $L1$-regularized Markov blanket. We then introduce a novel scoring function which infers the candidate causes for each variable through its Markov blanket. The lasso regression between each variable (as response variable) and its candidate causes (as predictors) is used to obtain a directed graph. We finally remove the cycles using the simulated annealing (SA) algorithm for achieving a DAG. Experimental results over well-known DAGs indicate that proposed method has higher accuracy and better degree of data matching.

KEYWORDS:

• Directed acyclic graph
• $L1$-regularized Markov blanket
• causal relations
• LASSO regression

Acknowledgments

We would like to thank two anonymous referees and an associate editor for their constructive comments and suggestions. Vahid Rezaei Tabar is grateful to the Department of Statistics at Allameh Tabataba'i University (No. 040/ h/ p, July 15, 2017).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been supported by the Polish National Science Centre (2014/15/B/ST6/05082), Foundation for Polish Science (TEAM to DP) and by a grant from the Department of Science and Technology, India under Indo-Polish/Polish-Indo project No.: DST/INT/POL/P-36/2016. The work was co-supported by grant 1U54DK107967-01 Nucleome Positioning System for Spatiotemporal Genome Organization and Regulation within 4DNucleome NIH program.