Statistics and Computing

, Volume 26, Issue 4, pp 797–811 | Cite as

Exact estimation of multiple directed acyclic graphs

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

Abstract

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.

Keywords

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

Notes

Acknowledgments

The authors are grateful to Dr. Ricardo Silva and two anonymous reviewers, whose feedback helped to improve the paper. CJO was supported by the Centre for Research in Statistical Methodology (CRiSM) EPSRC EP /D002060/1. JC was supported by the Medical Research Council (Project Grant G1002312). SM was supported by the UK Medical Research Council and is a recipient of a Royal Society Wolfson Research Merit Award. The authors are grateful to Lilia Carneiro da Costa and Tom Nichols who collaborated in the analysis of fMRI data and to Mark Bartlett who provided technical support with GOBNILP. The authors also thank Diane Oyen and several other colleagues who provided feedback on an earlier draft.

Supplementary material

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

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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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