{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T16:08:43Z","timestamp":1782835723237,"version":"3.54.5"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T00:00:00Z","timestamp":1630454400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T00:00:00Z","timestamp":1630454400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Front. Comput. Sci."],"published-print":{"date-parts":[[2021,12]]},"DOI":"10.1007\/s11704-020-0268-6","type":"journal-article","created":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T16:03:28Z","timestamp":1630512208000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["BIC-based node order learning for improving Bayesian network structure learning"],"prefix":"10.1007","volume":"15","author":[{"given":"Yali","family":"Lv","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junzhong","family":"Miao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiye","family":"Liang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ling","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuhua","family":"Qian","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,9,1]]},"reference":[{"key":"268_CR1","volume-title":"Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference","author":"P Judea","year":"1988","unstructured":"Judea P. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers, San Mateo, California, 1988"},{"issue":"5659","key":"268_CR2","doi-asserted-by":"publisher","first-page":"799","DOI":"10.1126\/science.1094068","volume":"303","author":"N Friedman","year":"2004","unstructured":"Friedman N. Inferring cellular networks using probabilistic graphical models. Science, 2004, 303(5659): 799\u2013805","journal-title":"Science"},{"issue":"6","key":"268_CR3","doi-asserted-by":"publisher","first-page":"788","DOI":"10.1093\/bioinformatics\/18.6.788","volume":"18","author":"A Raval","year":"2002","unstructured":"Raval A, Ghahramani Z, Wild D L. A Bayesian network model for protein fold and remote homologue recognition. Bioinformatics, 2002, 18(6): 788\u2013801","journal-title":"Bioinformatics"},{"issue":"7","key":"268_CR4","first-page":"1281","volume":"39","author":"W Chen","year":"2016","unstructured":"Chen W, Zhu B, Zhang H. BN-mapping: visual analysis of geospatial data with Bayesian network. Chinese Journal of Computers, 2016, 39(7): 1281\u20131293","journal-title":"Chinese Journal of Computers"},{"issue":"5","key":"268_CR5","doi-asserted-by":"publisher","first-page":"1760","DOI":"10.1016\/j.patcog.2014.12.004","volume":"48","author":"P Peng","year":"2015","unstructured":"Peng P, Tian Y, Wang Y, Li J, Huang T. Robust multiple cameras pedestrian detection with multi-view Bayesian network. Pattern Recognition, 2015, 48(5): 1760\u20131772","journal-title":"Pattern Recognition"},{"key":"268_CR6","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1016\/j.patcog.2017.02.028","volume":"68","author":"L Liu","year":"2017","unstructured":"Liu L, Wang S, Su G, Huang Z, Liu M. Towards complex activity recognition using a Bayesian network-based probabilistic generative framework. Pattern Recognition, 2017, 68: 295\u2013309","journal-title":"Pattern Recognition"},{"issue":"4","key":"268_CR7","doi-asserted-by":"publisher","first-page":"569","DOI":"10.1016\/S0957-4174(03)00097-6","volume":"25","author":"G Oatley","year":"2003","unstructured":"Oatley G, Ewart B. Crimes analysis software: \u2018pins in maps\u2019, clustering and Bayes net prediction. Expert Systems with Applications, 2003, 25(4): 569\u2013588","journal-title":"Expert Systems with Applications"},{"key":"268_CR8","unstructured":"Chickering D M, Heckerman D, Meek C. Learning Bayesian networks is NP-hard. Technical Report, MSR-TR-94-17, Microsoft Research, Microsoft Corporation, 1994"},{"key":"268_CR9","first-page":"1287","volume":"5","author":"D M Chickering","year":"2004","unstructured":"Chickering D M, Heckerman D, Meek C. Large-sample learning of Bayesian networks is NP-hard. Journal of Machine Learning Research, 2004, 5: 1287\u20131330","journal-title":"Journal of Machine Learning Research"},{"key":"268_CR10","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1016\/j.cam.2015.02.055","volume":"287","author":"H Bouhamed","year":"2015","unstructured":"Bouhamed H, Masmoudi A, Lecroq T, Rebai A. Structure space of Bayesian networks is dramatically reduced by subdividing it in subnetworks. Journal of Computational and Applied Mathematics, 2015, 287: 48\u201362","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"268_CR11","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/BF00994016","volume":"20","author":"D Heckerman","year":"1995","unstructured":"Heckerman D, Geiger D, Chickering D M. Learning Bayesian networks: the combination of knowledge and statistical data. Machine Learning, 1995, 20: 197\u2013243","journal-title":"Machine Learning"},{"issue":"3","key":"268_CR12","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1111\/j.1467-8640.1994.tb00166.x","volume":"10","author":"W Lam","year":"1994","unstructured":"Lam W, Bacchus F. Learning Bayesian belief networks: an approach based on the MDL principle. Computational Intelligence, 1994, 10(3): 269\u2013293","journal-title":"Computational Intelligence"},{"key":"268_CR13","doi-asserted-by":"publisher","first-page":"1209","DOI":"10.1007\/s10994-018-5701-9","volume":"107","author":"M Scanagatta","year":"2018","unstructured":"Scanagatta M, Corani G, De Campos C P, Zaffalon M. Approximate structure learning for large Bayesian networks. Machine Learning, 2018, 107: 1209\u20131227","journal-title":"Machine Learning"},{"key":"268_CR14","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1016\/j.artint.2018.04.002","volume":"260","author":"C P De Campos","year":"2018","unstructured":"De Campos C P, Scanagatta M, Corani G, Zaffalon M. Entropy-based pruning for learning Bayesian networks using BIC. Artificial Intelligence, 2018, 260: 42\u201350","journal-title":"Artificial Intelligence"},{"key":"268_CR15","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1007\/BF00994110","volume":"9","author":"G F Cooper","year":"1992","unstructured":"Cooper G F, Herskovits E H. A Bayesian method for the induction of probabilistic networks from data. Machine Learning, 1992, 9: 309\u2013347","journal-title":"Machine Learning"},{"key":"268_CR16","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1016\/j.ijar.2018.02.004","volume":"95","author":"M Scanagatta","year":"2018","unstructured":"Scanagatta M, Corani G, Zaffalon M, Yoo J, Kang U. Efficient learning of bounded-treewidth Bayesian networks from complete and incomplete data sets. International Journal of Approximate Reasoning, 2018, 95: 152\u2013166","journal-title":"International Journal of Approximate Reasoning"},{"key":"268_CR17","doi-asserted-by":"crossref","unstructured":"Nie S, De Campos C P, Ji Q. Learning Bayesian networks with bounded treewidth via guided search. In: Proceedings of the 30th AAAI Conference on Artificial Intelligence. 2016, 3294\u20133300","DOI":"10.1609\/aaai.v30i1.10418"},{"key":"268_CR18","unstructured":"Parviainen P, Farahani H S, Lagergren J. Learning bounded treewidth Bayesian networks using integer linear programming. In: Proceedings of the 17th International Conference on Artificial Intelligence and Statistics. 2014, 751\u2013759"},{"key":"268_CR19","first-page":"2699","volume":"9","author":"G Elidan","year":"2008","unstructured":"Elidan G, Gould S. Learning bounded treewidth Bayesian networks. Journal of Machine Learning Research, 2008, 9: 2699\u20132731","journal-title":"Journal of Machine Learning Research"},{"issue":"1","key":"268_CR20","first-page":"2002","volume":"17","author":"T Niinimaki","year":"2016","unstructured":"Niinimaki T, Parviainen P, Koivisto M. Structure discovery in Bayesian networks by sampling partial orders. Journal of Machine Learning Research, 2016, 17(1): 2002\u20132048","journal-title":"Journal of Machine Learning Research"},{"key":"268_CR21","unstructured":"Teyssier M, Koller D. Ordering-based search: a simple and effective algorithm for learning Bayesian networks. In: Proceedings of the 21st Conference on Uncertainty in Artificial Intelligence. 2005, 584\u2013590"},{"key":"268_CR22","first-page":"1855","volume":"28","author":"M Scanagatta","year":"2015","unstructured":"Scanagatta M, De Campos C P, Corani G, Zaffalon M. Learning Bayesian networks with thousands of variables. Neural Information Processing Systems, 2015, 28: 1855\u20131863","journal-title":"Neural Information Processing Systems"},{"issue":"5","key":"268_CR23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TKDE.2008.59","volume":"20","author":"X Chen","year":"2008","unstructured":"Chen X, Anantha G, Lin X. Improving Bayesian network structure learning with mutual information-based node ordering in the K2 algorithm. IEEE Transactions on Knowledge and Data Engineering, 2008, 20(5): 1\u201313","journal-title":"IEEE Transactions on Knowledge and Data Engineering"},{"key":"268_CR24","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1016\/j.patrec.2013.12.021","volume":"40","author":"S Ko","year":"2014","unstructured":"Ko S, Kim D. An efficient node ordering method using the conditional frequency for the K2 algorithm. Pattern Recognition Letters, 2014, 40: 80\u201387","journal-title":"Pattern Recognition Letters"},{"key":"268_CR25","unstructured":"Hsu W H, Guo H, Perry B B, Stilson J A. A permutation genetic algorithm for variable ordering in learning Bayesian networks from data. In: Proceedings of the Genetic and Evolutionary Computation Conference. 2002, 383\u2013390"},{"key":"268_CR26","first-page":"1","volume":"18","author":"Y W Park","year":"2017","unstructured":"Park Y W, Klabjan D. Bayesian network learning via topological order. Journal of Machine Learning Research, 2017, 18: 1\u201332","journal-title":"Journal of Machine Learning Research"},{"key":"268_CR27","unstructured":"Zhang L, Guo H. Introduction to Bayesian Networks. Science Press, 2006"},{"issue":"3\u20134","key":"268_CR28","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1016\/S0888-613X(98)10014-2","volume":"19","author":"N L Zhang","year":"1998","unstructured":"Zhang N L, Yan L. Independence of causal influence and clique tree propagation. International Journal of Approximate Reasoning, 1998, 19(3\u20134): 335\u2013349","journal-title":"International Journal of Approximate Reasoning"},{"key":"268_CR29","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1613\/jair.2842","volume":"37","author":"R Mateescu","year":"2010","unstructured":"Mateescu R, Kask K, Gogate V, Dechter R. Join-graph propagation algorithms. Journal of Artificial Intelligence Research, 2010, 37: 279\u2013328","journal-title":"Journal of Artificial Intelligence Research"},{"key":"268_CR30","first-page":"1","volume":"17","author":"R J Goudie","year":"2016","unstructured":"Goudie R J, Mukherjee S. A Gibbs sampler for learning DAGs. Journal of Machine Learning Research, 2016, 17: 1\u201339","journal-title":"Journal of Machine Learning Research"},{"key":"268_CR31","doi-asserted-by":"publisher","first-page":"66","DOI":"10.1016\/j.artint.2018.11.007","volume":"274","author":"M Benjumeda","year":"2019","unstructured":"Benjumeda M, Bielza C, Larranaga P. Learning tractable Bayesian networks in the space of elimination orders. Artificial Intelligence, 2019, 274: 66\u201390","journal-title":"Artificial Intelligence"},{"key":"268_CR32","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1016\/j.patcog.2019.02.025","volume":"91","author":"M Benjumeda","year":"2019","unstructured":"Benjumeda M, Luengosanchez S, Larranaga P, Bielza C. Tractable learning of Bayesian networks from partially observed data. Pattern Recognition, 2019, 91: 190\u2013199","journal-title":"Pattern Recognition"},{"key":"268_CR33","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/s10994-006-6889-7","volume":"65","author":"I Tsamardinos","year":"2006","unstructured":"Tsamardinos I, Brown L E, Aliferis C F. The max-min hill-climbing Bayesian network structure learning algorithm. Machine Learning, 2006, 65: 31\u201378","journal-title":"Machine Learning"},{"issue":"11","key":"268_CR34","first-page":"2558","volume":"54","author":"Y Lv","year":"2017","unstructured":"Lv Y, Wu J, Liang J, Qian Y. Random search learning algorithm of BN based on super-structure. Journal of Computer Research and Development, 2017, 54(11): 2558\u20132566","journal-title":"Journal of Computer Research and Development"},{"key":"268_CR35","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1016\/j.ijar.2019.08.004","volume":"114","author":"X Qi","year":"2019","unstructured":"Qi X, Fan X, Gao Y, Liu Y. Learning Bayesian network structures using weakest mutual-information-first strategy. International Journal of Approximate Reasoning, 2019, 114: 84\u201398","journal-title":"International Journal of Approximate Reasoning"},{"key":"268_CR36","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/j.ijar.2019.09.002","volume":"115","author":"T Talvitie","year":"2019","unstructured":"Talvitie T, Eggeling R, Koivisto M. Learning Bayesian networks with local structure, mixed variables, and exact algorithms. International Journal of Approximate Reasoning, 2019, 115: 69\u201395","journal-title":"International Journal of Approximate Reasoning"},{"key":"268_CR37","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1016\/j.ijar.2019.10.003","volume":"115","author":"M Scutari","year":"2019","unstructured":"Scutari M, Graafland C E, Guti\u00e9rrez J M. Who learns better Bayesian network structures: accuracy and speed of structure learning algorithms. International Journal of Approximate Reasoning, 2019, 115: 235\u2013253","journal-title":"International Journal of Approximate Reasoning"},{"key":"268_CR38","doi-asserted-by":"publisher","unstructured":"Ye Q L, Amini A A, Zhou Q. Optimizing regularized cholesky score for order-based learning of Bayesian networks. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2020, DOI: https:\/\/doi.org\/10.1109\/TPAMI.2020.2990820","DOI":"10.1109\/TPAMI.2020.2990820"},{"issue":"6","key":"268_CR39","doi-asserted-by":"publisher","first-page":"1157","DOI":"10.1109\/TKDE.2019.2899096","volume":"32","author":"S Lee","year":"2020","unstructured":"Lee S, Kim S B. Parallel simulated annealing with a greedy algorithm for Bayesian network structure learning. IEEE Transactions on Knowledge and Data Engineering, 2020, 32(6): 1157\u20131166","journal-title":"IEEE Transactions on Knowledge and Data Engineering"},{"key":"268_CR40","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1016\/j.artint.2015.05.007","volume":"244","author":"T Yao","year":"2017","unstructured":"Yao T, Choi A, Darwiche A. Learning Bayesian network parameters under equivalence constraints. Artificial Intelligence, 2017, 244: 239\u2013257","journal-title":"Artificial Intelligence"},{"key":"268_CR41","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/j.ijar.2005.10.005","volume":"42","author":"C Riggelsen","year":"2006","unstructured":"Riggelsen C. Learning parameters of Bayesian networks from incomplete data via importance sampling. International Journal of Approximate Reasoning, 2006, 42: 69\u201383","journal-title":"International Journal of Approximate Reasoning"},{"key":"268_CR42","first-page":"1357","volume":"7","author":"R S Niculescu","year":"2006","unstructured":"Niculescu R S, Mitchell T M, Rao R B. Bayesian network learning with parameter constraints. Journal of Machine Learning Research, 2006, 7: 1357\u20131383","journal-title":"Journal of Machine Learning Research"},{"key":"268_CR43","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1016\/j.patcog.2019.02.006","volume":"91","author":"Y Yang","year":"2019","unstructured":"Yang Y, Gao X, Guo Z, Chen D. Learning Bayesian networks using the constrained maximum a posteriori probability method. Pattern Recognition, 2019, 91: 123\u2013134","journal-title":"Pattern Recognition"},{"key":"268_CR44","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1016\/j.ijar.2017.10.024","volume":"93","author":"M Benjumeda","year":"2018","unstructured":"Benjumeda M, Bielza C, Larranaga P. Tractability of most probable explanations in multidimensional Bayesian network classifiers. International Journal of Approximate Reasoning, 2018, 93: 74\u201387","journal-title":"International Journal of Approximate Reasoning"},{"key":"268_CR45","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.knosys.2016.07.031","volume":"117","author":"A L Madsen","year":"2017","unstructured":"Madsen A L, Jensen F, Salmeron A, Langseth H, Nielsen T D. A parallel algorithm for Bayesian network structure learning from large data sets. Knowledge Based Systems, 2017, 117: 46\u201355","journal-title":"Knowledge Based Systems"},{"issue":"2","key":"268_CR46","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1137\/0608024","volume":"8","author":"S Arnborg","year":"1987","unstructured":"Arnborg S, Corneil D G, Proskurowski A. Complexity of finding embeddings in a k-tree. SIAM Journal on Algebraic Discrete Methods, 1987, 8(2): 277\u2013284","journal-title":"SIAM Journal on Algebraic Discrete Methods"},{"key":"268_CR47","first-page":"2285","volume":"27","author":"S Nie","year":"2014","unstructured":"Nie S, Maua D D, De Campos C P, Ji Q. Advances in learning Bayesian networks of bounded treewidth. Advances in Neural Information Processing Systems, 2014, 27: 2285\u20132293","journal-title":"Advances in Neural Information Processing Systems"},{"key":"268_CR48","doi-asserted-by":"publisher","first-page":"3046","DOI":"10.1016\/j.patcog.2009.04.006","volume":"42","author":"W Liao","year":"2009","unstructured":"Liao W, Ji Q. Learning Bayesian network parameters under incomplete data with domain knowledge. Pattern Recognition, 2009, 42: 3046\u20133056","journal-title":"Pattern Recognition"},{"issue":"4","key":"268_CR49","doi-asserted-by":"publisher","first-page":"348","DOI":"10.1504\/IJWMC.2018.093862","volume":"14","author":"Y Lv","year":"2018","unstructured":"Lv Y, Wu J, Jing T. Pqisem: BN\u2019s structure learning based on partial qualitative influences and SEM algorithm from missing data. International Journal of Wireless and Mobile Computing, 2018, 14(4): 348\u2013357","journal-title":"International Journal of Wireless and Mobile Computing"},{"key":"268_CR50","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1016\/j.ijar.2015.11.004","volume":"69","author":"A R Masegosa","year":"2016","unstructured":"Masegosa A R, Feelders A, Der Gaag L C. Learning from incomplete data in Bayesian networks with qualitative influences. International Journal of Approximate Reasoning, 2016, 69: 18\u201334","journal-title":"International Journal of Approximate Reasoning"}],"container-title":["Frontiers of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11704-020-0268-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11704-020-0268-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11704-020-0268-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,27]],"date-time":"2023-01-27T12:49:37Z","timestamp":1674823777000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11704-020-0268-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,1]]},"references-count":50,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["268"],"URL":"https:\/\/doi.org\/10.1007\/s11704-020-0268-6","relation":{},"ISSN":["2095-2228","2095-2236"],"issn-type":[{"value":"2095-2228","type":"print"},{"value":"2095-2236","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,1]]},"assertion":[{"value":"12 June 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 October 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 September 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"156337"}}