{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T16:02:44Z","timestamp":1778601764063,"version":"3.51.4"},"reference-count":52,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,3,31]],"date-time":"2021-03-31T00:00:00Z","timestamp":1617148800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100011033","name":"Agencia Estatal de Investigaci\u00f3n","doi-asserted-by":"publisher","award":["PID2019-106758GB-C33\/AEI\/10.13039\/501100011033"],"award-info":[{"award-number":["PID2019-106758GB-C33\/AEI\/10.13039\/501100011033"]}],"id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011033","name":"Agencia Estatal de Investigaci\u00f3n","doi-asserted-by":"publisher","award":["TIN2016\u201077902\u2010C3\u20101\u2010P"],"award-info":[{"award-number":["TIN2016\u201077902\u2010C3\u20101\u2010P"]}],"id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011698","name":"Junta de Comunidades de Castilla-La Mancha","doi-asserted-by":"publisher","award":["SBPLY\/17\/180501\/000493"],"award-info":[{"award-number":["SBPLY\/17\/180501\/000493"]}],"id":[{"id":"10.13039\/501100011698","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["FPU18\/00181"],"award-info":[{"award-number":["FPU18\/00181"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The goal of the Label Ranking (LR) problem is to learn preference models that predict the preferred ranking of class labels for a given unlabeled instance. Different well-known machine learning algorithms have been adapted to deal with the LR problem. In particular, fine-tuned instance-based algorithms (e.g., k-nearest neighbors) and model-based algorithms (e.g., decision trees) have performed remarkably well in tackling the LR problem. Probabilistic Graphical Models (PGMs, e.g., Bayesian networks) have not been considered to deal with this problem because of the difficulty of modeling permutations in that framework. In this paper, we propose a Hidden Naive Bayes classifier (HNB) to cope with the LR problem. By introducing a hidden variable, we can design a hybrid Bayesian network in which several types of distributions can be combined: multinomial for discrete variables, Gaussian for numerical variables, and Mallows for permutations. We consider two kinds of probabilistic models: one based on a Naive Bayes graphical structure (where only univariate probability distributions are estimated for each state of the hidden variable) and another where we allow interactions among the predictive attributes (using a multivariate Gaussian distribution for the parameter estimation). The experimental evaluation shows that our proposals are competitive with the start-of-the-art algorithms in both accuracy and in CPU time requirements.<\/jats:p>","DOI":"10.3390\/e23040420","type":"journal-article","created":{"date-parts":[[2021,3,31]],"date-time":"2021-03-31T10:24:33Z","timestamp":1617186273000},"page":"420","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Mixture-Based Probabilistic Graphical Models for the Label Ranking Problem"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7211-7051","authenticated-orcid":false,"given":"Enrique G.","family":"Rodrigo","sequence":"first","affiliation":[{"name":"Departamento de Sistemas Inform\u00e1ticos, Universidad de Castilla-La Mancha, 02071 Albacete, Spain"},{"name":"Laboratorio de Sistemas Inteligentes y Miner\u00eda de Datos, Instituto de Investigaci\u00f3n en Inform\u00e1tica de Albacete, 02071 Albacete, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1777-8540","authenticated-orcid":false,"given":"Juan C.","family":"Alfaro","sequence":"additional","affiliation":[{"name":"Departamento de Sistemas Inform\u00e1ticos, Universidad de Castilla-La Mancha, 02071 Albacete, Spain"},{"name":"Laboratorio de Sistemas Inteligentes y Miner\u00eda de Datos, Instituto de Investigaci\u00f3n en Inform\u00e1tica de Albacete, 02071 Albacete, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1786-8087","authenticated-orcid":false,"given":"Juan A.","family":"Aledo","sequence":"additional","affiliation":[{"name":"Laboratorio de Sistemas Inteligentes y Miner\u00eda de Datos, Instituto de Investigaci\u00f3n en Inform\u00e1tica de Albacete, 02071 Albacete, Spain"},{"name":"Departamento de Matem\u00e1ticas, Universidad de Castilla-La Mancha, 02071 Albacete, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1188-1117","authenticated-orcid":false,"given":"Jos\u00e9 A.","family":"G\u00e1mez","sequence":"additional","affiliation":[{"name":"Departamento de Sistemas Inform\u00e1ticos, Universidad de Castilla-La Mancha, 02071 Albacete, Spain"},{"name":"Laboratorio de Sistemas Inteligentes y Miner\u00eda de Datos, Instituto de Investigaci\u00f3n en Inform\u00e1tica de Albacete, 02071 Albacete, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Vembu, S., and G\u00e4rtner, T. 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