{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T23:08:49Z","timestamp":1762038529417,"version":"build-2065373602"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"10-11","license":[{"start":{"date-parts":[[2021,6,26]],"date-time":"2021-06-26T00:00:00Z","timestamp":1624665600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,6,26]],"date-time":"2021-06-26T00:00:00Z","timestamp":1624665600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Math Artif Intell"],"published-print":{"date-parts":[[2021,11]]},"DOI":"10.1007\/s10472-021-09754-2","type":"journal-article","created":{"date-parts":[[2021,6,26]],"date-time":"2021-06-26T00:02:13Z","timestamp":1624665733000},"page":"1035-1052","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Constraint-based learning for non-parametric continuous bayesian networks"],"prefix":"10.1007","volume":"89","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1623-064X","authenticated-orcid":false,"given":"Marvin","family":"Lasserre","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R\u00e9gis","family":"Lebrun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pierre-Henri","family":"Wuillemin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,6,26]]},"reference":[{"key":"9754_CR1","doi-asserted-by":"crossref","unstructured":"Baudin, M., Dutfoy, A., Iooss, B., Popelin, A.L.: Openturns: An industrial software for uncertainty quantification in simulation (2015)","DOI":"10.1007\/978-3-319-11259-6_64-1"},{"issue":"4","key":"9754_CR2","doi-asserted-by":"publisher","first-page":"1031","DOI":"10.1214\/aos\/1031689016","volume":"30","author":"T Bedford","year":"2002","unstructured":"Bedford, T., Cooke, R.M., et al.: Vines\u2013a new graphical model for dependent random variables. Ann. Stat. 30(4), 1031\u20131068 (2002)","journal-title":"Ann. Stat."},{"key":"9754_CR3","doi-asserted-by":"crossref","unstructured":"Beinlich, I.A., Suermondt, H.J., Chavez, R.M., Cooper, G.F.: The alarm monitoring system: A case study with two probabilistic inference techniques for belief networks. In: AIME 89, pp 247\u2013256. Springer (1989)","DOI":"10.1007\/978-3-642-93437-7_28"},{"key":"9754_CR4","unstructured":"Bouezmarni, T., Rombouts, J., Taamouti, A.: A nonparametric copula based test for conditional independence with applications to granger causality. Economics Working Papers. Universidad Carlos III, Departamento de Econom\u00eda (2009)"},{"issue":"1","key":"9754_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.jmva.2009.02.014","volume":"101","author":"T Bouezmarni","year":"2010","unstructured":"Bouezmarni, T., Rombouts, J.V., Taamouti, A.: Asymptotic properties of the bernstein density copula estimator for \u03b1-mixing data. J. Multivar. Anal. 101(1), 1\u201310 (2010). https:\/\/doi.org\/10.1016\/j.jmva.2009.02.014","journal-title":"J. Multivar. Anal."},{"issue":"1","key":"9754_CR6","first-page":"3741","volume":"15","author":"D Colombo","year":"2014","unstructured":"Colombo, D., Maathuis, M.H.: Order-independent constraint-based causal structure learning. J. Machine Learn. Res. 15(1), 3741\u20133782 (2014)","journal-title":"J. Machine Learn. Res."},{"key":"9754_CR7","doi-asserted-by":"crossref","unstructured":"Czado, C.: Pair-copula constructions of multivariate copulas. In: Copula Theory and Its Applications, pp 93\u2013109 (2010)","DOI":"10.1007\/978-3-642-12465-5_4"},{"issue":"1","key":"9754_CR8","first-page":"274","volume":"65","author":"P Deheuvels","year":"1979","unstructured":"Deheuvels, P.: La Fonction de d\u00e9pendance Empirique et Ses Propri\u00e9t\u00e9s. Un test Non Param\u00e9trique D\u2019Ind\u00e9pendance. Bulletins de l\u2019Acad\u00e9mie Royale de Belgique 65(1), 274\u2013292 (1979)","journal-title":"Bulletins de l\u2019Acad\u00e9mie Royale de Belgique"},{"key":"9754_CR9","unstructured":"Elidan, G.: Copula bayesian networks. In: Advances in Neural Information Processing Systems, pp 559\u2013567 (2010)"},{"issue":"4","key":"9754_CR10","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1061\/(ASCE)1084-0699(2007)12:4(347)","volume":"12","author":"C Genest","year":"2007","unstructured":"Genest, C., Favre, A.C.: Everything you always wanted to know about copula modeling but were afraid to ask. J. Hydrol. Eng. 12(4), 347\u2013368 (2007)","journal-title":"J. Hydrol. Eng."},{"key":"9754_CR11","doi-asserted-by":"publisher","first-page":"2093","DOI":"10.1007\/978-1-4613-0303-9_33","volume-title":"Tabu Search","author":"F Glover","year":"1998","unstructured":"Glover, F., Laguna, M.: Tabu Search, pp 2093\u20132229. Springer, Boston (1998). https:\/\/doi.org\/10.1007\/978-1-4613-0303-9_33"},{"key":"9754_CR12","unstructured":"Gonzales, C., Torti, L., Wuillemin, P.H.: aGrUM: A graphical universal model framework. In: International Conference on Industrial Engineering, Other Applications of Applied Intelligent Systems, Proceedings of the 30th International Conference on Industrial Engineering, Other Applications of Applied Intelligent Systems. Arras, France. https:\/\/hal.archives-ouvertes.fr\/hal-01509651 (2017)"},{"key":"9754_CR13","unstructured":"Huang, J.C.: Cumulative distribution networks: Inference, estimation and applications of graphical models for cumulative distribution functions. Citeseer (2009)"},{"key":"9754_CR14","doi-asserted-by":"crossref","unstructured":"Ide, J.S., Cozman, F.G.: Random generation of bayesian networks. In: Brazilian Symposium on Artificial Intelligence, pp 366\u2013376. Springer (2002)","DOI":"10.1007\/3-540-36127-8_35"},{"key":"9754_CR15","doi-asserted-by":"crossref","unstructured":"Joe, H.: Multivariate models and multivariate dependence concepts. CRC Press (1997)","DOI":"10.1201\/b13150"},{"key":"9754_CR16","unstructured":"Karra, K., Mili, L.: Hybrid copula bayesian networks. In: Conference on Probabilistic Graphical Models, pp 240\u2013251 (2016)"},{"key":"9754_CR17","unstructured":"Koller, D., Friedman, N.: Probabilistic graphical models: principles and techniques. MIT Press (2009)"},{"key":"9754_CR18","doi-asserted-by":"crossref","unstructured":"Lasserre, M., Lebrun, R., Wuillemin, P.H.: Learning continuous high-dimensional models using mutual information and copula bayesian networks (2021)","DOI":"10.1609\/aaai.v35i13.17441"},{"key":"9754_CR19","doi-asserted-by":"crossref","unstructured":"Lauritzen, S.L., Wermuth, N.: Graphical models for associations between variables, some of which are qualitative and some quantitative. Annals Stat. 31\u201357 (1989)","DOI":"10.1214\/aos\/1176347003"},{"key":"9754_CR20","doi-asserted-by":"crossref","unstructured":"Lindskog, F., McNeil, A., Schmock, U.: Kendall\u2019s tau for elliptical distributions. In: Credit Risk, pp 149\u2013156. Springer (2003)","DOI":"10.1007\/978-3-642-59365-9_8"},{"key":"9754_CR21","volume-title":"An introduction to copulas","author":"RB Nelsen","year":"2007","unstructured":"Nelsen, R.B.: An introduction to copulas. Springer Science & Business Media, New York (2007)"},{"issue":"4","key":"9754_CR22","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1080\/03610928308831068","volume":"22","author":"PJ Rousseeuw","year":"1993","unstructured":"Rousseeuw, P.J., Molenberghs, G.: Transformation of non positive semidefinite correlation matrices. Commun. Stat. Theor. Methods 22(4), 965\u2013984 (1993)","journal-title":"Commun. Stat. Theor. Methods"},{"issue":"03","key":"9754_CR23","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1017\/S026646660420305X","volume":"20","author":"A Sancetta","year":"2004","unstructured":"Sancetta, A., Satchell, S.: The bernstein copula and its applications to modeling and approximations of multivariate distributions. Econ. Theor. 20(03), 535\u2013562 (2004)","journal-title":"Econ. Theor."},{"issue":"2","key":"9754_CR24","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1214\/aos\/1176344136","volume":"6","author":"G Schwarz","year":"1978","unstructured":"Schwarz, G.: Estimating the dimension of a model. Annals Stat. 6 (2), 461\u2013464 (1978)","journal-title":"Annals Stat."},{"key":"9754_CR25","first-page":"229","volume":"8","author":"A Sklar","year":"1959","unstructured":"Sklar, A.: Fonctions de r\u00e9partition \u00e0 n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8, 229\u2013231 (1959)","journal-title":"Publ. Inst. Statist. Univ. Paris"},{"key":"9754_CR26","doi-asserted-by":"crossref","unstructured":"Spirtes, P., Glymour, C.N., Scheines, R., Heckerman, D., Meek, C., Cooper, G., Richardson, T.: Causation, prediction, and search. MIT Press (2000)","DOI":"10.7551\/mitpress\/1754.001.0001"},{"issue":"4","key":"9754_CR27","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1017\/S0266466608080341","volume":"24","author":"L Su","year":"2008","unstructured":"Su, L., White, H.: A nonparametric hellinger metric test for conditional independence. Econ. Theor. 24(4), 829\u2013864 (2008)","journal-title":"Econ. Theor."},{"key":"9754_CR28","doi-asserted-by":"publisher","first-page":"664","DOI":"10.1016\/j.jcp.2014.05.002","volume":"272","author":"J Wan","year":"2014","unstructured":"Wan, J., Zabaras, N.: A probabilistic graphical model based stochastic input model construction. J. Comput. Physics 272, 664\u2013685 (2014)","journal-title":"J. Comput. Physics"}],"container-title":["Annals of Mathematics and Artificial Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10472-021-09754-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10472-021-09754-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10472-021-09754-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T15:49:09Z","timestamp":1672588149000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10472-021-09754-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,26]]},"references-count":28,"journal-issue":{"issue":"10-11","published-print":{"date-parts":[[2021,11]]}},"alternative-id":["9754"],"URL":"https:\/\/doi.org\/10.1007\/s10472-021-09754-2","relation":{},"ISSN":["1012-2443","1573-7470"],"issn-type":[{"type":"print","value":"1012-2443"},{"type":"electronic","value":"1573-7470"}],"subject":[],"published":{"date-parts":[[2021,6,26]]},"assertion":[{"value":"19 May 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 June 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Conflict of Interests"}}]}}