{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:25:17Z","timestamp":1760243117804,"version":"build-2065373602"},"reference-count":46,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2015,7,21]],"date-time":"2015-07-21T00:00:00Z","timestamp":1437436800000},"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>This work presents a new general purpose classifier named Averaged Extended Tree Augmented Naive Bayes (AETAN), which is based on combining the advantageous characteristics of Extended Tree Augmented Naive Bayes (ETAN) and Averaged One-Dependence Estimator (AODE) classifiers. We describe the main properties of the approach and algorithms for learning it, along with an analysis of its computational time complexity. Empirical results with numerous data sets indicate that the new approach is superior to ETAN and AODE in terms of both zero-one classification accuracy and log loss. It also compares favourably against weighted AODE and hidden Naive Bayes. The learning phase of the new approach is slower than that of its competitors, while the time complexity for the testing phase is similar. Such characteristics suggest that the new classifier is ideal in scenarios where online learning is not required.<\/jats:p>","DOI":"10.3390\/e17075085","type":"journal-article","created":{"date-parts":[[2015,7,21]],"date-time":"2015-07-21T10:17:48Z","timestamp":1437473868000},"page":"5085-5100","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Averaged Extended Tree Augmented Naive Classifier"],"prefix":"10.3390","volume":"17","author":[{"given":"Aaron","family":"Meehan","sequence":"first","affiliation":[{"name":"EEECS, Queen's University Belfast, University Road, Belfast BT7 1NN, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cassio","family":"De Campos","sequence":"additional","affiliation":[{"name":"EEECS, Queen's University Belfast, University Road, Belfast BT7 1NN, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,7,21]]},"reference":[{"key":"ref_1","unstructured":"Cheng, J., and Greiner, R. (August, January 30). Comparing Bayesian Network Classifiers, Stockholm, Sweden."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1023\/A:1007465528199","article-title":"Bayesian Network Classifiers","volume":"29","author":"Friedman","year":"1997","journal-title":"Mach. Learn."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan Kaufmann.","DOI":"10.1016\/B978-0-08-051489-5.50008-4"},{"key":"ref_4","unstructured":"Koller, D., and Friedman, N. (2009). Probabilistic Graphical Models, MIT Press."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Chickering, D.M. (1996). Learning Bayesian Networks is NP-Complete, Springer.","DOI":"10.1007\/978-1-4612-2404-4_12"},{"key":"ref_6","first-page":"1287","article-title":"Large-Sample Learning of Bayesian Networks is NP-Hard","volume":"5","author":"Chickering","year":"2004","journal-title":"J. Mach. Learn. Res."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Pernkopf, F., and Bilmes, J. (2005, January 7\u201311). Discriminative versus generative parameter and structure learning of Bayesian network classifiers, Bonn, Germany.","DOI":"10.1145\/1102351.1102434"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"464","DOI":"10.1016\/j.patcog.2012.08.007","article-title":"Stochastic margin-based structure learning of Bayesian network classifiers","volume":"46","author":"Pernkopf","year":"2013","journal-title":"Pattern Recognit."},{"key":"ref_9","first-page":"2323","article-title":"Efficient Heuristics for Discriminative Structure Learning of Bayesian Network Classifiers","volume":"11","author":"Pernkopf","year":"2010","journal-title":"J. Mach. Learn. Res."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Grossman, D., and Domingos, P. (2004, January 1\u20134). Learning Bayesian network classifiers by maximizing conditional likelihood, Banff, AB, Canada.","DOI":"10.1145\/1015330.1015339"},{"key":"ref_11","unstructured":"De Campos, C.P., Cuccu, M., Corani, G., and Zaffalon, M. Extended Tree Augmented Naive Classifier, Springer, Switzerland."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"De Campos, C.P., Corani, G., Scanagatta, M., Cuccu, M., and Zaffalon, M. (2015). Learning Extended Tree Augmented Naive Structures. Int. J. Approx. Reason., in press.","DOI":"10.1007\/978-3-319-11433-0_12"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s10994-005-4258-6","article-title":"Not So Naive Bayes: Aggregating One-Dependence Estimators","volume":"58","author":"Webb","year":"2005","journal-title":"Mach. Learn."},{"key":"ref_14","unstructured":"Keogh, E., and Pazzani, M.J. (1999, January 4\u20136). Learning Augmented Bayesian Classifiers: A Comparison of Distribution-Based and Classification-Based Approaches, Fort Lauderdale, FL, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"5433","DOI":"10.1016\/j.eswa.2015.02.049","article-title":"Not always simple classification: Learning SuperParent for class probability estimation","volume":"42","author":"Qiu","year":"2015","journal-title":"Expert Syst. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/j.knosys.2011.08.010","article-title":"Improving tree augmented naive Bayes for class probability estimation","volume":"26","author":"Jiang","year":"2012","journal-title":"Knowl.-Based Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1016\/j.patrec.2010.11.016","article-title":"Random one-dependence estimators","volume":"32","author":"Jiang","year":"2011","journal-title":"Pattern Recognit. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Buntine, W. (1991, January 13\u201315). Theory refinement on Bayesian networks, Los Angeles, CA, USA.","DOI":"10.1016\/B978-1-55860-203-8.50010-3"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/BF00994110","article-title":"A Bayesian method for the induction of probabilistic networks from data","volume":"9","author":"Cooper","year":"1992","journal-title":"Mach. Learn."},{"key":"ref_20","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_21","unstructured":"De Campos, C.P., and Ji, Q. (2010, January 11\u201315). Properties of Bayesian Dirichlet Scores to Learn Bayesian Network Structures, Atlanta, GA, USA."},{"key":"ref_22","unstructured":"Silander, T., and Myllymaki, P. (2006, January 13\u201316). A simple approach for finding the globally optimal Bayesian network structure, Cambridge, MA, USA."},{"key":"ref_23","first-page":"663","article-title":"Efficient Structure Learning of Bayesian Networks Using Constraints","volume":"12","author":"Ji","year":"2011","journal-title":"J. Mach. Learn. Res."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1613\/jair.4039","article-title":"Learning Optimal Bayesian Networks: A Shortest Path Perspective","volume":"48","author":"Yuan","year":"2013","journal-title":"J. Artif. Intell. Res."},{"key":"ref_25","unstructured":"Barlett, M., and Cussens, J. (2013, January 11\u201315). Advances in Bayesian Network Learning Using Integer Programming. Bellevue, WA, USA."},{"key":"ref_26","unstructured":"Dasgupta, S. (August, January 30). Learning polytrees, Stockholm, Sweden."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1023\/A:1007413511361","article-title":"On the optimality of the simple Bayesian classifier under zero-one loss","volume":"29","author":"Domingos","year":"1997","journal-title":"Mach. Learn."},{"key":"ref_28","first-page":"385","article-title":"Idiot\u2019s Bayes-Not So Stupid after All?","volume":"69","author":"Hand","year":"2001","journal-title":"Int. Stat. Rev."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1023\/A:1009778005914","article-title":"On bias, variance, 0\/1\u2014loss, and the curse-of-dimensionality","volume":"1","author":"Friedman","year":"1997","journal-title":"Data Min. Knowl. Discov."},{"key":"ref_30","unstructured":"Corani, G., de Campos, C.P., and Sun, Y. (2009, January 14\u201318). A tree augmented classifier based on Extreme Imprecise Dirichlet Model. Durham, UK."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1053","DOI":"10.1016\/j.ijar.2010.08.007","article-title":"A tree augmented classifier based on Extreme Imprecise Dirichlet Model","volume":"51","author":"Corani","year":"2010","journal-title":"Int. J. Approx. Reason."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/j.knosys.2008.10.006","article-title":"On the classification performance of TAN and general Bayesian networks","volume":"22","author":"Madden","year":"2009","journal-title":"Knowl.-Based Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1109\/TIT.1968.1054142","article-title":"Approximating discrete probability distributions with dependence trees","volume":"14","author":"Chow","year":"1968","journal-title":"IEEE Trans. Inf. Theory."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"233","DOI":"10.6028\/jres.071B.032","article-title":"Optimum Branchings","volume":"71B","author":"Edmonds","year":"1967","journal-title":"J. Res. Natl. Bureau Stand. B"},{"key":"ref_35","first-page":"1396","article-title":"On the Shortest Arborescence of a Directed Graph","volume":"14","author":"Chu","year":"1965","journal-title":"Sci. Sin."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1214\/aoms\/1177729694","article-title":"On information and sufficiency","volume":"22","author":"Kullback","year":"1951","journal-title":"Ann. Math. Stat."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1002\/net.3230070103","article-title":"Finding Optimum Branchings","volume":"7","author":"Tarjan","year":"1977","journal-title":"Networks"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1002\/net.3230090403","article-title":"A note on finding optimum branchings","volume":"9","author":"Camerini","year":"1979","journal-title":"Networks"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1080\/0952813X.2011.639092","article-title":"Weighted average of one dependence estimators","volume":"24","author":"Jiang","year":"2012","journal-title":"J. Exp. Theor. Artif. Intell."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.1109\/TKDE.2008.234","article-title":"A novel Bayes model: Hidden naive Bayes","volume":"21","author":"Jiang","year":"2009","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_41","unstructured":"Available online: http:\/\/www.cs.waikato.ac.nz\/ml\/weka\/."},{"key":"ref_42","unstructured":"Witten, I.H., and Frank, E. (2005). Data Mining: Practical Machine Learning Tools and Techniques, Morgan Kaufmann. [2nd ed.]."},{"key":"ref_43","unstructured":"De Campos, C.P., and Benavoli, A. (2011, January 16\u201322). Inference with multinomial data: Why to weaken the prior strength, Barcelona, Spain."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Scanagatta, M., de Campos, C.P., and Zaffalon, M. (2014, January 17\u201319). Min-BDeu and Max-BDeu Scores for Learning Bayesian Networks, Utrecht, The Netherlands.","DOI":"10.1007\/978-3-319-11433-0_28"},{"key":"ref_45","unstructured":"Silander, T., Kontkanen, P., and Myllym\u00e4ki, P. (2007, January 19\u201322). On Sensitivity of the MAP Bayesian Network Structure to the Equivalent Sample Size Parameter, Vancouver, BC, Canada."},{"key":"ref_46","unstructured":"Asuncion, A., and Newman, D.J. Available online: http:\/\/www.ics.uci.edu\/~mlearn\/MLRepository.html."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/7\/5085\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:49:30Z","timestamp":1760215770000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/7\/5085"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,7,21]]},"references-count":46,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2015,7]]}},"alternative-id":["e17075085"],"URL":"https:\/\/doi.org\/10.3390\/e17075085","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2015,7,21]]}}}