{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T01:51:51Z","timestamp":1775872311217,"version":"3.50.1"},"reference-count":24,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,8,20]],"date-time":"2018-08-20T00:00:00Z","timestamp":1534723200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Bayesian network structure learning from data has been proved to be a NP-hard (Non-deterministic Polynomial-hard) problem. An effective method of improving the accuracy of Bayesian network structure is using experts\u2019 knowledge instead of only using data. Some experts\u2019 knowledge (named here explicit knowledge) can make the causal relationship between nodes in Bayesian Networks (BN) structure clear, while the others (named here vague knowledge) cannot. In the previous algorithms for BN structure learning, only the explicit knowledge was used, but the vague knowledge, which was ignored, is also valuable and often exists in the real world. Therefore we propose a new method of using more comprehensive experts\u2019 knowledge based on hybrid structure learning algorithm, a kind of two-stage algorithm. Two types of experts\u2019 knowledge are defined and incorporated into the hybrid algorithm. We formulate rules to generate better initial network structure and improve the scoring function. Furthermore, we take expert level difference and opinion conflict into account. Experimental results show that our proposed method can improve the structure learning performance.<\/jats:p>","DOI":"10.3390\/e20080620","type":"journal-article","created":{"date-parts":[[2018,8,20]],"date-time":"2018-08-20T11:23:06Z","timestamp":1534764186000},"page":"620","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["A Hybrid Structure Learning Algorithm for Bayesian Network Using Experts\u2019 Knowledge"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4700-962X","authenticated-orcid":false,"given":"Hongru","family":"Li","sequence":"first","affiliation":[{"name":"Information Science and Engineering, Northeastern University, P.O. Box 135, No. 11 St. 3, Wenhua Road, Heping District, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6695-2982","authenticated-orcid":false,"given":"Huiping","family":"Guo","sequence":"additional","affiliation":[{"name":"Information Science and Engineering, Northeastern University, P.O. Box 135, No. 11 St. 3, Wenhua Road, Heping District, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,20]]},"reference":[{"key":"ref_1","unstructured":"Jensen, F.V. (1996). An Introduction to Bayesian Networks, Springer."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1109\/69.868904","article-title":"Constructing Bayesian networks for medical diagnosis from vague and partially correct statistics","volume":"12","author":"Nikovski","year":"2000","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_3","first-page":"53","article-title":"Monitoring and diagnosis of a multistage manufacturing process using Bayesian networks","volume":"14","author":"Wolbrecht","year":"1998","journal-title":"Ai Edam"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1016\/j.ijpe.2016.07.007","article-title":"A Bayesian network model for resilience-based supplier selection","volume":"180","author":"Hosseini","year":"2016","journal-title":"Int. J. Prod. Econ."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.jmsy.2016.09.006","article-title":"A general framework for assessing system resilience using Bayesian networks: A case study of sulfuric acid manufacturer","volume":"41","author":"Hosseini","year":"2016","journal-title":"J. Manuf. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1016\/j.cie.2016.01.007","article-title":"Modeling infrastructure resilience using Bayesian networks: A case study of inland waterway ports","volume":"93","author":"Hosseini","year":"2016","journal-title":"Comput. Ind. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2134","DOI":"10.1016\/j.patrec.2012.06.013","article-title":"Learning Bayesian network structure using Markov blanket decomposition","volume":"33","author":"Bui","year":"2012","journal-title":"Pattern Recognit. Lett."},{"key":"ref_8","first-page":"8","article-title":"Investigation of the impacts of constraint-based algorithms to the quality of Bayesian network structure in hybrid algorithms for medical studies","volume":"5","author":"Cengiz","year":"2014","journal-title":"J. Adv. Sci. Res."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.ipl.2008.03.015","article-title":"Approximation algorithms for restricted Bayesian network structures","volume":"108","author":"Ziegler","year":"2008","journal-title":"Inf. Process. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/S0888-613X(02)00091-9","article-title":"Ant colony optimization for learning Bayesian networks","volume":"31","author":"Campos","year":"2002","journal-title":"Int. J. Approx. Reason."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s10994-006-6889-7","article-title":"The max-min hill-climbing Bayesian network structure learning algorithm","volume":"65","author":"Tsamardinos","year":"2006","journal-title":"Mach. Learn."},{"key":"ref_12","first-page":"2251","article-title":"Finding optimal Bayesian network given a super-structure","volume":"9","author":"Perrier","year":"2012","journal-title":"J. Mach. Learn. Res."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/S0888-613X(01)00041-X","article-title":"A hybrid methodology for learning belief networks: Benedict","volume":"27","author":"Acid","year":"2001","journal-title":"Int. J. Approx. Reason."},{"key":"ref_14","unstructured":"Li, S., Zhang, J., Sun, B., and Lei, J. (June, January 31). An incremental structure learning approach for Bayesian network. Proceedings of the 26th Chinese Control and Decision Conference, Changsha, China."},{"key":"ref_15","first-page":"121","article-title":"Learning Bayesian networks is NP-hard","volume":"112","author":"Chickering","year":"1994","journal-title":"Networks"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1007\/s11390-015-1556-8","article-title":"A structure learning algorithm for Bayesian network using prior knowledge","volume":"30","author":"Xu","year":"2015","journal-title":"J. Comput. Sci. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2154","DOI":"10.1109\/TPAMI.2016.2636828","article-title":"Exploiting experts\u2019 knowledge for structure learning of Bayesian networks","volume":"39","author":"Amirkhani","year":"2016","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/BF00994016","article-title":"Learning Bayesian networks: The combination of knowledge and statistical data","volume":"20","author":"Heckerman","year":"1995","journal-title":"Mach. Learn."},{"key":"ref_19","unstructured":"Chen, J., Jia, H., Huang, Y., and Liu, D. (2012, January 15\u201317). Learning the structure of dynamic Bayesian network with domain knowledge. Proceedings of the International Conference on Machine Learning and Cybernetics, Xi\u2019an, China."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Murphy, K.P. (2018, August 19). An Introduction to Graphical Models. Available online: http:\/\/www2.denizyuret.com\/ref\/murphy\/intro_gm.pdf.","DOI":"10.1093\/oso\/9780198796916.003.0001"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/j.neucom.2013.02.015","article-title":"Improved heuristic equivalent search algorithm based on maximal information coefficient for bayesian network structure learning","volume":"117","author":"Zhang","year":"2013","journal-title":"Neurocomputing"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Robinson, R.W. (1977). Counting Unlabeled Acyclic Digraphs, Springer.","DOI":"10.1007\/BFb0069178"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.swevo.2012.09.002","article-title":"S-shaped versus v-shaped transfer functions for binary particle swarm optimization","volume":"9","author":"Mirjalili","year":"2013","journal-title":"Swarm Evol. Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.ijar.2006.06.009","article-title":"Bayesian Network Learning Algorithms Using Structural Restrictions","volume":"45","author":"Campos","year":"2007","journal-title":"Int. J. Approx. Reason."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/8\/620\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:19:48Z","timestamp":1760195988000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/8\/620"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,20]]},"references-count":24,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2018,8]]}},"alternative-id":["e20080620"],"URL":"https:\/\/doi.org\/10.3390\/e20080620","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,20]]}}}