{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T03:47:10Z","timestamp":1778557630942,"version":"3.51.4"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2016,11,4]],"date-time":"2016-11-04T00:00:00Z","timestamp":1478217600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001824","name":"Czech Science Foundation","doi-asserted-by":"publisher","award":["13-20012S"],"award-info":[{"award-number":["13-20012S"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000265","name":"UK Medical Research Council","doi-asserted-by":"crossref","award":["G1002312"],"award-info":[{"award-number":["G1002312"]}],"id":[{"id":"10.13039\/501100000265","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100004040","name":"KU Leuven","doi-asserted-by":"publisher","award":["SF\/14\/008"],"award-info":[{"award-number":["SF\/14\/008"]}],"id":[{"id":"10.13039\/501100004040","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001824","name":"Czech Science Foundation","doi-asserted-by":"crossref","award":["16-12010S"],"award-info":[{"award-number":["16-12010S"]}],"id":[{"id":"10.13039\/501100001824","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2017,7]]},"DOI":"10.1007\/s10107-016-1087-2","type":"journal-article","created":{"date-parts":[[2016,11,4]],"date-time":"2016-11-04T17:48:21Z","timestamp":1478281701000},"page":"285-324","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Polyhedral aspects of score equivalence in Bayesian network structure learning"],"prefix":"10.1007","volume":"164","author":[{"given":"James","family":"Cussens","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Haws","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6038-629X","authenticated-orcid":false,"given":"Milan","family":"Studen\u00fd","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,11,4]]},"reference":[{"key":"1087_CR1","unstructured":"Bartlett, M., Cussens, J.: Advances in Bayesian network learning using integer programming. In: Nicholson, A., Smyth, P. (eds.) Uncertainty in Artificial Intelligence, vol. 29, pp. 182\u2013191. AUAI Press, Corvallis (2013)"},{"key":"1087_CR2","volume-title":"A Course in Convexity. Graduate Studies in Mathematics","author":"A Barvinok","year":"2002","unstructured":"Barvinok, A.: A Course in Convexity. Graduate Studies in Mathematics, vol. 54. American Mathematical Society, Providence (2002)"},{"key":"1087_CR3","unstructured":"Bouckaert, R.R.: Bayesian belief networks\u2014from construction to evidence. Ph.D. thesis, University of Utrecht (1995)"},{"key":"1087_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1148-8","volume-title":"An Introduction to Convex Polytopes","author":"A Br\u00f8ndsted","year":"1983","unstructured":"Br\u00f8ndsted, A.: An Introduction to Convex Polytopes. Springer, New York (1983)"},{"key":"1087_CR5","unstructured":"Chickering, D.M.: A transformational characterization of equivalent Bayesian network structures. In: Besnard, P., Hanks, S. (eds.) Uncertainty in Artificial Intelligence, vol. 11, pp. 87\u201398. Morgan Kaufmann, San Francisco (1995)"},{"key":"1087_CR6","first-page":"505","volume":"3","author":"DM Chickering","year":"2002","unstructured":"Chickering, D.M.: Optimal structure identification with greedy search. J. Mach. Learn. Res. 3, 505\u2013554 (2002)","journal-title":"J. Mach. Learn. Res."},{"key":"1087_CR7","unstructured":"Cussens, J.: Maximum likelihood pedigree reconstruction using integer programming. In: Proceedings of the Workshop on Constraint Based Methods for Bioinformatics (WCBMB), pp. 9\u201319 (2010)"},{"key":"1087_CR8","unstructured":"Cussens, J.: Bayesian network learning with cutting planes. In: Cozman, F., Pfeffer, A. (eds.) Uncertainty in Artificial Intelligence, vol. 27, pp. 153\u2013160, AUAI Press, Corvallis (2011)"},{"key":"1087_CR9","unstructured":"Cussens, J., Bartlett, M.: GOBNILP software (2016). www.cs.york.ac.uk\/aig\/sw\/gobnilp\/"},{"key":"1087_CR10","unstructured":"Cussens, J., J\u00e4rvisalo, M., Korhonen, J.H., Bartlett, M.: Bayesian network structure learning with integer programming: polytopes, facets, and complexity. J. Artif. Intell. Res. (2016). arXiv:1605.04071"},{"key":"1087_CR11","first-page":"663","volume":"12","author":"CP Campos de","year":"2011","unstructured":"de Campos, C.P., Ji, Q.: Efficient structure learning Bayesian networks using constraints. J. Mach. Learn. Res. 12, 663\u2013689 (2011)","journal-title":"J. Mach. Learn. Res."},{"key":"1087_CR12","doi-asserted-by":"crossref","first-page":"1336","DOI":"10.1016\/j.ijar.2012.04.001","volume":"53","author":"R Hemmecke","year":"2012","unstructured":"Hemmecke, R., Lindner, S., Studen\u00fd, M.: Characteristic imsets for learning Bayesian network structure. Int. J. Approx. Reason. 53, 1336\u20131349 (2012)","journal-title":"Int. J. Approx. Reason."},{"key":"1087_CR13","unstructured":"Jaakkola, T., Sontag, D., Globerson, A., Meila, M.: Learning Bayesian network structure using LP relaxations. In: Journal of Machine Learning Research Workshop and Conference Proceedings, AISTATS 2010, vol. 9, pp. 358\u2013365 (2010)"},{"key":"1087_CR14","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198522195.001.0001","volume-title":"Graphical Models","author":"SL Lauritzen","year":"1996","unstructured":"Lauritzen, S.L.: Graphical Models. Clarendon Press, Oxford (1996)"},{"key":"1087_CR15","volume-title":"Learning Bayesian Networks","author":"RE Neapolitan","year":"2004","unstructured":"Neapolitan, R.E.: Learning Bayesian Networks. Pearson Prentice Hall, Upper Saddle River (2004)"},{"key":"1087_CR16","unstructured":"Orlinskaya G.: Linear constraints on standard and characteristic imsets for learning Bayesian network structures. Diploma thesis, TU Munich (2014)"},{"key":"1087_CR17","volume-title":"Matroid Theory","author":"JG Oxley","year":"1992","unstructured":"Oxley, J.G.: Matroid Theory. Oxford University Press, Oxford (1992)"},{"key":"1087_CR18","volume-title":"Probabilistic Reasoning in Intelligent Systems","author":"J Pearl","year":"1988","unstructured":"Pearl, J.: Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, San Mateo (1988)"},{"key":"1087_CR19","volume-title":"Probabilistic Conditional Independence Structures","author":"M Studen\u00fd","year":"2005","unstructured":"Studen\u00fd, M.: Probabilistic Conditional Independence Structures. Springer, London (2005)"},{"key":"1087_CR20","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1016\/j.ijar.2010.01.014","volume":"51","author":"M Studen\u00fd","year":"2010","unstructured":"Studen\u00fd, M., Vomlel, J., Hemmecke, R.: A geometric view on learning Bayesian network structures. Int. J. Approx. Reason. 51, 573\u2013586 (2010)","journal-title":"Int. J. Approx. Reason."},{"key":"1087_CR21","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1016\/j.ijar.2010.09.004","volume":"52","author":"M Studen\u00fd","year":"2011","unstructured":"Studen\u00fd, M., Vomlel, J.: On open questions in the geometric approach to structural learning Bayesian nets. Int. J. Approx. Reason. 52, 627\u2013640 (2011)","journal-title":"Int. J. Approx. Reason."},{"key":"1087_CR22","doi-asserted-by":"crossref","first-page":"59","DOI":"10.18409\/jas.v4i1.19","volume":"4","author":"M Studen\u00fd","year":"2013","unstructured":"Studen\u00fd, M., Haws, D.C.: On polyhedral approximations of polytopes for learning Bayesian networks. J. Algebr. Stat. 4, 59\u201392 (2013)","journal-title":"J. Algebr. Stat."},{"key":"1087_CR23","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1016\/j.ijar.2013.09.016","volume":"55","author":"M Studen\u00fd","year":"2014","unstructured":"Studen\u00fd, M., Haws, D.: Learning Bayesian network structure: towards the essential graph by integer linear programming tools. Int. J. Approx. Reason. 55, 1043\u20131071 (2014)","journal-title":"Int. J. Approx. Reason."},{"key":"1087_CR24","unstructured":"Studen\u00fd, M.: How matroids occur in the context of learning Bayesian network structures. In: Meila, M., Heskes, T. (eds.) Uncertainty in Artificial Intelligence, vol. 31, pp. 832\u2013841. AUAI Press, Corvallis (2015)"},{"key":"1087_CR25","unstructured":"Studen\u00fd, M., Kroupa, T.: Core-based criterion for extreme supermodular functions. Discrete Appl. Math. 206, 122\u2013151 (2016)"},{"key":"1087_CR26","volume-title":"Integer Programming","author":"LA Wolsey","year":"1998","unstructured":"Wolsey, L.A.: Integer Programming. Wiley, New York (1998)"},{"key":"1087_CR27","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-8431-1","volume-title":"Lectures on Polytopes","author":"GM Ziegler","year":"1995","unstructured":"Ziegler, G.M.: Lectures on Polytopes. Springer, New York (1995)"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-016-1087-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-016-1087-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-016-1087-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,20]],"date-time":"2024-06-20T10:51:08Z","timestamp":1718880668000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-016-1087-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,11,4]]},"references-count":27,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2017,7]]}},"alternative-id":["1087"],"URL":"https:\/\/doi.org\/10.1007\/s10107-016-1087-2","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,11,4]]}}}