Voting-based ensemble learning for partial lexicographic preference forests over combinatorial domains
We study preference representation models based on partial lexicographic preference trees (PLP-trees). We propose to represent preference relations as forests of small PLP-trees (PLP-forests), and to use voting rules to aggregate orders represented by the individual trees into a single order to be t...
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| Veröffentlicht in: | Annals of mathematics and artificial intelligence Jg. 87; H. 1-2; S. 137 - 155 |
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| Abstract | We study preference representation models based on partial lexicographic preference trees (PLP-trees). We propose to represent preference relations as forests of small PLP-trees (PLP-forests), and to use voting rules to aggregate orders represented by the individual trees into a single order to be taken as a model of the agent’s preference relation. We show that when learned from examples, PLP-forests have better accuracy than single PLP-trees. We also show that the choice of a voting rule does not have a major effect on the aggregated order, thus rendering the problem of selecting the “right” rule less critical. Next, for the proposed PLP-forest preference models, we develop methods to compute optimal and near-optimal outcomes, the tasks that appear difficult for some other common preference models. Lastly, we compare our models with those based on decision trees, which brings up questions for future research. |
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| AbstractList | We study preference representation models based on partial lexicographic preference trees (PLP-trees). We propose to represent preference relations as forests of small PLP-trees (PLP-forests), and to use voting rules to aggregate orders represented by the individual trees into a single order to be taken as a model of the agent’s preference relation. We show that when learned from examples, PLP-forests have better accuracy than single PLP-trees. We also show that the choice of a voting rule does not have a major effect on the aggregated order, thus rendering the problem of selecting the “right” rule less critical. Next, for the proposed PLP-forest preference models, we develop methods to compute optimal and near-optimal outcomes, the tasks that appear difficult for some other common preference models. Lastly, we compare our models with those based on decision trees, which brings up questions for future research. We study preference representation models based on partial lexicographic preference trees (PLP-trees). We propose to represent preference relations as forests of small PLP-trees (PLP-forests), and to use voting rules to aggregate orders represented by the individual trees into a single order to be taken as a model of the agent's preference relation. We show that when learned from examples, PLP-forests have better accuracy than single PLP-trees. We also show that the choice of a voting rule does not have a major effect on the aggregated order, thus rendering the problem of selecting the "right" rule less critical. Next, for the proposed PLP-forest preference models, we develop methods to compute optimal and near-optimal outcomes, the tasks that appear difficult for some other common preference models. Lastly, we compare our models with those based on decision trees, which brings up questions for future research. Keywords Lexicographic preference models * Preference learning * Preference modeling and reasoning * Social choice theory * Computational complexity theory * Voting theory * Maximum satisfiability Mathematics Subject Classification (2010) 68T30 |
| Audience | Academic |
| Author | Liu, Xudong Truszczynski, Miroslaw |
| Author_xml | – sequence: 1 givenname: Xudong orcidid: 0000-0002-5149-5539 surname: Liu fullname: Liu, Xudong email: xudong.liu@unf.edu organization: School of Computing, University of North Florida – sequence: 2 givenname: Miroslaw surname: Truszczynski fullname: Truszczynski, Miroslaw organization: Department of Computer Science, University of Kentucky |
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| Cites_doi | 10.1016/j.mathsocsci.2008.12.010 10.1007/BF01075297 10.1609/aaai.v24i1.7545 10.1609/aaai.v29i1.9403 10.1007/978-3-642-33558-7_69 10.1007/978-3-319-90050-6_16 10.1007/978-3-642-24873-3_13 10.1016/j.ejor.2016.08.055 10.1007/s10601-016-9245-y 10.1017/S0007123400006542 10.1007/978-3-642-41575-3_19 10.1023/A:1015551010381 10.24963/ijcai.2017/182 10.1023/A:1010933404324 10.1007/978-3-319-23114-3_2 |
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| Keywords | Voting theory Maximum satisfiability Preference modeling and reasoning Preference learning Computational complexity theory 68T30 Lexicographic preference models Social choice theory |
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| References | Mattei, N.: Empirical evaluation of voting rules with strictly ordered preference data. In: International Conference on Algorithmic Decisiontheory, pp 165–177. Springer (2011) Liu, X., Truszczynski, M.: Aggregating conditionally lexicographic preferences using answer set programming solvers. In: Proceedings of the 3rd International Conference on Algorithmic Decision Theory, pp 244–258. Springer (2013) Ansótegui, C., Bonet, M.L., Levy, J.: A new algorithm for weighted partial maxsat. In: Fox, M., Poole, D. (eds.) Proceedings of the 24th AAAI Conference on Artificial Intelligence. AAAI Press (2010) Myers, J.L., Well, A., Lorch, R.F.: Research design and statistical analysis. Routledge (2010) BreimanLRandom forestsMach. Learn.200145153210.1023/A:1010933404324 GehrleinWVCondorcet’s paradox and the likelihood of its occurrence: different perspectives on balanced preferencesTheor. Decis.2002522171199192602910.1023/A:1015551010381 Wilson, N., George, A.: Efficient inference and computation of optimal alternatives for preference languages based on lexicographic models. In: Sierra, C. (ed.) Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI 2017, pp 1311–1317 (2017) Booth, R., Chevaleyre, Y., Lang, J., Mengin, J., Sombattheera, C.: Learning conditionally lexicographic preference relations. In: ECAI, pp 269–274 (2010) FelsenthalDSMaozZRapoportAAn empirical evaluation of six voting procedures: do they really make any difference?Br. J. Polit. Sci.1993230112710.1017/S0007123400006542 Liu, X., Truszczynski, M.: Learning partial lexicographic preference trees and forests over multi-valued attributes. In: Proceedings of the 2nd Global Conference on Artificial Intelligence (GCAI-16), EPiC Series in Computing, vol. 41, pp 314–328. EasyChair (2016) BräuningMHüllermeierEKellerTGlaumMLexicographic preferences for predictive modeling of human decision making: a new machine learning method with an application in accountingEur. J. Oper. Res.20172581295306358139110.1016/j.ejor.2016.08.055 Lang, J., Mengin, J., Xia, L.: Aggregating conditionally lexicographic preferences on multi-issue domains. In: Principles and Practice of Constraint Programming, pp 973–987. Springer (2012) Liu, X., Truszczynski, M.: Preference learning and optimization for partial lexicographic preference forests over combinatorial domains. In: Proceedings of the 10th International Symposium on Foundations of Information and Knowledge Systems. Springer (2018) Schmitt, M., Martignon, L.: Complexity of lexicographic strategies on binary cues. Preprint (1999) LangJXiaLSequential composition of voting rules in multi-issue domainsMath. Soc. Sci.2009573304324251261610.1016/j.mathsocsci.2008.12.010 FraserNMOrdinal preference representationsTheor. Decis.1994361456710.1007/BF01075297 Liu, X., Truszczynski, M.: Learning partial lexicographic preference trees over combinatorial domains. In: Proceedings of the 29th AAAI Conference on Artificial Intelligence, pp 1539–1545. AAAI Press (2015) Wilson, N.: Preference inference based on lexicographic models. In: Schaub, T., Friedrich, G., O’Sullivan, B. (eds.) Proceedings of the 21st European Conference on Artificial Intelligence, ECAI 2014, Frontiers in Artificial Intelligence and Applications, vol. 263, pp 921–926. IOS Press (2014) Liu, X., Truszczynski, M.: Reasoning with Preference Trees over Combinatorial Domains. In: Algorithmic Decision Theory, pp 19–34. Springer (2015) Allen, J., Moussa, A., Liu, X.: Human-in-the-loop learning of qualitative preference models. In: The 32Nd International Florida Artificial Intelligence Research Society Conference. AAAI Press (2019) HurleyBO’SullivanBAlloucheDKatsirelosGSchiexTZytnickiMDe GivrySMulti-language evaluation of exact solvers in graphical model discrete optimizationConstraints2016213413434350036210.1007/s10601-016-9245-y L Breiman (9645_CR5) 2001; 45 9645_CR2 9645_CR10 9645_CR21 9645_CR3 J Lang (9645_CR11) 2009; 57 9645_CR20 M Bräuning (9645_CR4) 2017; 258 9645_CR1 DS Felsenthal (9645_CR6) 1993; 23 WV Gehrlein (9645_CR8) 2002; 52 9645_CR19 NM Fraser (9645_CR7) 1994; 36 9645_CR14 B Hurley (9645_CR9) 2016; 21 9645_CR13 9645_CR12 9645_CR18 9645_CR17 9645_CR16 9645_CR15 |
| References_xml | – reference: BräuningMHüllermeierEKellerTGlaumMLexicographic preferences for predictive modeling of human decision making: a new machine learning method with an application in accountingEur. J. Oper. Res.20172581295306358139110.1016/j.ejor.2016.08.055 – reference: Mattei, N.: Empirical evaluation of voting rules with strictly ordered preference data. In: International Conference on Algorithmic Decisiontheory, pp 165–177. Springer (2011) – reference: Liu, X., Truszczynski, M.: Learning partial lexicographic preference trees over combinatorial domains. In: Proceedings of the 29th AAAI Conference on Artificial Intelligence, pp 1539–1545. AAAI Press (2015) – reference: Myers, J.L., Well, A., Lorch, R.F.: Research design and statistical analysis. Routledge (2010) – reference: GehrleinWVCondorcet’s paradox and the likelihood of its occurrence: different perspectives on balanced preferencesTheor. Decis.2002522171199192602910.1023/A:1015551010381 – reference: Wilson, N.: Preference inference based on lexicographic models. In: Schaub, T., Friedrich, G., O’Sullivan, B. (eds.) Proceedings of the 21st European Conference on Artificial Intelligence, ECAI 2014, Frontiers in Artificial Intelligence and Applications, vol. 263, pp 921–926. IOS Press (2014) – reference: FelsenthalDSMaozZRapoportAAn empirical evaluation of six voting procedures: do they really make any difference?Br. J. Polit. Sci.1993230112710.1017/S0007123400006542 – reference: Liu, X., Truszczynski, M.: Learning partial lexicographic preference trees and forests over multi-valued attributes. In: Proceedings of the 2nd Global Conference on Artificial Intelligence (GCAI-16), EPiC Series in Computing, vol. 41, pp 314–328. EasyChair (2016) – reference: Allen, J., Moussa, A., Liu, X.: Human-in-the-loop learning of qualitative preference models. In: The 32Nd International Florida Artificial Intelligence Research Society Conference. AAAI Press (2019) – reference: Booth, R., Chevaleyre, Y., Lang, J., Mengin, J., Sombattheera, C.: Learning conditionally lexicographic preference relations. In: ECAI, pp 269–274 (2010) – reference: Schmitt, M., Martignon, L.: Complexity of lexicographic strategies on binary cues. Preprint (1999) – reference: Liu, X., Truszczynski, M.: Aggregating conditionally lexicographic preferences using answer set programming solvers. In: Proceedings of the 3rd International Conference on Algorithmic Decision Theory, pp 244–258. Springer (2013) – reference: LangJXiaLSequential composition of voting rules in multi-issue domainsMath. Soc. Sci.2009573304324251261610.1016/j.mathsocsci.2008.12.010 – reference: Ansótegui, C., Bonet, M.L., Levy, J.: A new algorithm for weighted partial maxsat. In: Fox, M., Poole, D. (eds.) Proceedings of the 24th AAAI Conference on Artificial Intelligence. AAAI Press (2010) – reference: Liu, X., Truszczynski, M.: Preference learning and optimization for partial lexicographic preference forests over combinatorial domains. In: Proceedings of the 10th International Symposium on Foundations of Information and Knowledge Systems. Springer (2018) – reference: Lang, J., Mengin, J., Xia, L.: Aggregating conditionally lexicographic preferences on multi-issue domains. In: Principles and Practice of Constraint Programming, pp 973–987. Springer (2012) – reference: Liu, X., Truszczynski, M.: Reasoning with Preference Trees over Combinatorial Domains. In: Algorithmic Decision Theory, pp 19–34. Springer (2015) – reference: BreimanLRandom forestsMach. Learn.200145153210.1023/A:1010933404324 – reference: FraserNMOrdinal preference representationsTheor. Decis.1994361456710.1007/BF01075297 – reference: Wilson, N., George, A.: Efficient inference and computation of optimal alternatives for preference languages based on lexicographic models. In: Sierra, C. (ed.) Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, IJCAI 2017, pp 1311–1317 (2017) – reference: HurleyBO’SullivanBAlloucheDKatsirelosGSchiexTZytnickiMDe GivrySMulti-language evaluation of exact solvers in graphical model discrete optimizationConstraints2016213413434350036210.1007/s10601-016-9245-y – volume: 57 start-page: 304 issue: 3 year: 2009 ident: 9645_CR11 publication-title: Math. Soc. Sci. doi: 10.1016/j.mathsocsci.2008.12.010 – volume: 36 start-page: 45 issue: 1 year: 1994 ident: 9645_CR7 publication-title: Theor. Decis. doi: 10.1007/BF01075297 – ident: 9645_CR2 doi: 10.1609/aaai.v24i1.7545 – ident: 9645_CR13 doi: 10.1609/aaai.v29i1.9403 – ident: 9645_CR10 doi: 10.1007/978-3-642-33558-7_69 – ident: 9645_CR16 doi: 10.1007/978-3-319-90050-6_16 – ident: 9645_CR17 doi: 10.1007/978-3-642-24873-3_13 – volume: 258 start-page: 295 issue: 1 year: 2017 ident: 9645_CR4 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2016.08.055 – volume: 21 start-page: 413 issue: 3 year: 2016 ident: 9645_CR9 publication-title: Constraints doi: 10.1007/s10601-016-9245-y – ident: 9645_CR18 – ident: 9645_CR19 – ident: 9645_CR15 – ident: 9645_CR3 – volume: 23 start-page: 1 issue: 01 year: 1993 ident: 9645_CR6 publication-title: Br. J. Polit. Sci. doi: 10.1017/S0007123400006542 – ident: 9645_CR12 doi: 10.1007/978-3-642-41575-3_19 – volume: 52 start-page: 171 issue: 2 year: 2002 ident: 9645_CR8 publication-title: Theor. Decis. doi: 10.1023/A:1015551010381 – ident: 9645_CR21 doi: 10.24963/ijcai.2017/182 – volume: 45 start-page: 5 issue: 1 year: 2001 ident: 9645_CR5 publication-title: Mach. Learn. doi: 10.1023/A:1010933404324 – ident: 9645_CR1 – ident: 9645_CR20 – ident: 9645_CR14 doi: 10.1007/978-3-319-23114-3_2 |
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| SubjectTerms | Accuracy Analysis Artificial Intelligence Cognition & reasoning Combinatorial analysis Complex Systems Computer Science Decision making Decision theory Decision trees Ensemble learning Forests and forestry Majority rule Mathematics Optimization Preferences Voting |
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| Title | Voting-based ensemble learning for partial lexicographic preference forests over combinatorial domains |
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