Abstract
We consider the problem of eliciting a model for ordered classification. In particular, we consider Majority Rule Sorting (MR-sort), a popular model for multiple criteria decision analysis, based on pairwise comparisons between alternatives and idealized profiles representing the “limit” of each category.
Our interactive elicitation protocol asks, at each step, the decision maker to classify an alternative; these assignments are used as training set for learning the model. Since we wish to limit the cognitive burden of elicitation, we aim at asking informative questions in order to find a good approximation of the optimal classification in a limited number of elicitation steps. We propose efficient strategies for computing the next question and show how its computation can be formulated as a linear program. We present experimental results showing the effectiveness of our approach.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
This step is of course only to be performed in simulations, in real use of the procedure the classification error will not be known.
- 2.
All experiments were run on a 2.9 GHz Intel, Core i7 and 16 Giga of RAM.
References
Ah-Pine, J., Mayag, B., Rolland, A.: Identification of a 2-additive bi-capacity by using mathematical programming. In: Perny, P., Pirlot, M., Tsoukiàs, A. (eds.) ADT 2013. LNCS (LNAI), vol. 8176, pp. 15–29. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-41575-3_2
Benabbou, N., Perny, P., Viappiani, P.: A regret-based preference elicitation approach for sorting with multicriteria reference profiles. In: From Multicriteria Decision Making to Preference Learning (DA2PL 2016) (2016)
Benabbou, N., Perny, P., Viappiani, P.: Incremental elicitation of choquet capacities for multicriteria choice, ranking and sorting problems. Artif. Intell. 246 , 152–180 (2017)
Boutilier, C.: Computational decision support: regret-based models for optimization and preference elicitation. In: Crowley, P.H. Zentall, T.R. (eds.) Comparative Decision Making: Analysis and Support Across Disciplines and Applications, pp. 423–453 (2013)
Bouyssou, D., Marchant, T.: An axiomatic approach to noncompensatory sorting methods in MCDM, II: more than two categories. Eur. J. Oper. Res. 178 (1), 246–276 (2007)
Conitzer, V., Sandholm, T.: Vote elicitation: complexity and strategy-proofness. In: AAAI/IAAI, pp. 392–397 (2002)
Domshlak, C., Hüllermeier, E., Kaci, S., Prade, H.: Preferences in AI: an overview (2011)
Dua, D., Graff, C.: UCI machine learning repository (2017)
Frank, E., Hall, M.: A simple approach to ordinal classification. In: De Raedt, L., Flach, P. (eds.) ECML 2001. LNCS (LNAI), vol. 2167, pp. 145–156. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44795-4_13
Fürnkranz, J., Hüllermeier, E.: Preference Learning, 1st edn. Springer, Boston (2010). https://doi.org/10.1007/978-0-387-30164-8
Fürnkranz, J., Hüllermeier, E., Mencía, E.L., Brinker, K.: Multilabel classification via calibrated label ranking. Mach. Learn. 73 (2), 133–153 (2008)
Gajos, K., Weld, D.S.: Preference elicitation for interface optimization. In: Proceedings of UIST, pp. 173–182. ACM (2005)
Greco, S., Mousseau, V., Slowinski, R.: Ordinal regression revisited: multiple criteria ranking using a set of additive value functions. Eur. J. Oper. Res. 191 (2), 416–436 (2008)
Jacquet-Lagrèze, E., Siskos, Y.: Assessing a set of additive utility functions for multicriteria decision making: the UTA method. Eur. J. Oper. Res. 10 , 151–164 (1982)
Leroy, A., Mousseau, V., Pirlot, M.: Learning the parameters of a multiple criteria sorting method. In: Brafman, R.I., Roberts, F.S., Tsoukiàs, A. (eds.) ADT 2011. LNCS (LNAI), vol. 6992, pp. 219–233. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-24873-3_17
Mousseau, V., Slowinski, R., Zielniewicz, P.: A user-oriented implementation of the ELECTRE-TRI method integrating preference elicitation support. Comput. OR 27 (7–8), 757–777 (2000)
Murphy, K.P.: Machine Learning: A Probabilistic Perspective. The MIT Press, Cambridge (2012)
Olteanu, A.L.: Strategies for the incremental inference of majority-rule sorting models. In: DA2PL 2018: from Multiple Criteria Decision Aid to Preference Learning, Poznan, Poland, November 2018
Roy, B.: The outranking approach and the foundations of electre methods. In: Bana e Costa, C.A. (ed.) Readings in Multiple Criteria Decision Aid, pp. 155–183. Springer, Heidelberg (1990). https://doi.org/10.1007/978-3-642-75935-2_8
Sobrie, O., Mousseau, V., Pirlot, M.: Learning a majority rule model from large sets of assignment examples. In: Perny, P., Pirlot, M., Tsoukiàs, A. (eds.) ADT 2013. LNCS (LNAI), vol. 8176, pp. 336–350. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-41575-3_26
Sobrie, O., Mousseau, V., Pirlot, M.: Learning the parameters of a non compensatory sorting model. In: Walsh, T. (ed.) ADT 2015. LNCS (LNAI), vol. 9346, pp. 153–170. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23114-3_10
Sobrie, O., Mousseau, V., Pirlot, M.: A population-based algorithm for learning a majority rule sorting model with coalitional veto. In: Trautmann, H., et al. (eds.) EMO 2017. LNCS, vol. 10173, pp. 575–589. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-54157-0_39
Sobrie, O., Mousseau, V., Pirlot, M.: Learning monotone preferences using a majority rule sorting model. Int. Trans. Oper. Res. 26 (5), 1786–1809 (2019)
Soufiani, H.A., Parkes, D.C., Xia, L.: Preference elicitation for general random utility models. arXiv preprint arXiv:1309.6864 (2013)
Teso, S., Passerini, A., Viappiani, P.: Constructive preference elicitation by setwise max-margin learning. In: Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence, IJCAI 2016, New York, NY, USA, 9–15 July 2016, pp. 2067–2073 (2016)
Teso, S., Passerini, A., Viappiani, P.: Constructive preference elicitation for multiple users with setwise max-margin. In: Rothe, J. (ed.) ADT 2017. LNCS (LNAI), vol. 10576, pp. 3–17. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67504-6_1
Zhao, Z., et al.: A cost-effective framework for preference elicitation and aggregation. arXiv preprint arXiv:1805.05287 (2018)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Nefla, O., Öztürk, M., Viappiani, P., Brigui-Chtioui, I. (2019). Interactive Elicitation of a Majority Rule Sorting Model with Maximum Margin Optimization. In: Pekeč, S., Venable, K.B. (eds) Algorithmic Decision Theory. ADT 2019. Lecture Notes in Computer Science(), vol 11834. Springer, Cham. https://doi.org/10.1007/978-3-030-31489-7_10
Download citation
DOI: https://doi.org/10.1007/978-3-030-31489-7_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-31488-0
Online ISBN: 978-3-030-31489-7
eBook Packages: Computer ScienceComputer Science (R0)