Bayesian Network Learning via Topological Order

Young Woong Park, Diego Klabjan

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We propose a mixed integer programming (MIP) model and iterative algorithms based on topological orders to solve optimization problems with acyclic constraints on a directed graph. The proposed MIP model has a significantly lower number of constraints compared to popular MIP models based on cycle elimination constraints and triangular inequalities. The proposed iterative algorithms use gradient descent and iterative reordering approaches, respectively, for searching topological orders. A computational experiment is presented for the Gaussian Bayesian network learning problem, an optimization problem minimizing the sum of squared errors of regression models with L1 penalty over a feature network with application of gene network inference in bioinformatics.

Original languageEnglish (US)
Pages (from-to)1-32
Number of pages32
JournalJournal of Machine Learning Research
StatePublished - Oct 1 2017


  • Bayesian networks
  • Directed acyclic graphs
  • Gaussian Bayesian network
  • Topological orders

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence


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