Statistics and Computing

, Volume 26, Issue 4, pp 797–811

Exact estimation of multiple directed acyclic graphs

  • Chris J. Oates
  • Jim Q. Smith
  • Sach Mukherjee
  • James Cussens

DOI: 10.1007/s11222-015-9570-9

Cite this article as:
Oates, C.J., Smith, J.Q., Mukherjee, S. et al. Stat Comput (2016) 26: 797. doi:10.1007/s11222-015-9570-9


This paper considers structure learning for multiple related directed acyclic graph (DAG) models. Building on recent developments in exact estimation of DAGs using integer linear programming (ILP), we present an ILP approach for joint estimation over multiple DAGs. Unlike previous work, we do not require that the vertices in each DAG share a common ordering. Furthermore, we allow for (potentially unknown) dependency structure between the DAGs. Results are presented on both simulated data and fMRI data obtained from multiple subjects.


Hierarchical model Bayesian network  Multiregression dynamical model Integer linear programming Joint estimation 

Supplementary material

11222_2015_9570_MOESM1_ESM.pdf (358 kb)
Supplementary material 1 (pdf 357 KB)

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Chris J. Oates
    • 1
    • 4
  • Jim Q. Smith
    • 1
  • Sach Mukherjee
    • 2
    • 5
  • James Cussens
    • 3
  1. 1.Department of StatisticsUniversity of WarwickCoventryUK
  2. 2.MRC Biostatistics Unit and CRUK Cambridge InstituteUniversity of CambridgeCambridgeUK
  3. 3.Department of Computer Science and York Centre for Complex Systems AnalysisUniversity of YorkYorkUK
  4. 4.School of Mathematical and Physical SciencesUniversity of Technology SydneySydneyAustralia
  5. 5.German Center for Neurodegenerative Diseases (DZNE)BonnGermany

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