Abstract
We consider the problem of statistical inference for ranking data, namely the problem of estimating a probability distribution on the permutation space. Since observed rankings could be incomplete in the sense of not comprising all choice alternatives, we propose to tackle the problem as one of learning from imprecise or coarse data. To this end, we associate an incomplete ranking with its set of consistent completions. We instantiate and compare two likelihood-based approaches that have been proposed in the literature for learning from set-valued data, the marginal and the so-called face-value likelihood. Concretely, we analyze a setting in which the underlying distribution is Plackett-Luce and observations are given in the form of pairwise comparisons.
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References
Marden JI (1995) Analyzing and modeling rank data. Chapman and Hall, London, New York
Liu TY (2011) Learning to rank for information retrieval. Springer
Fürnkranz J, Hüllermeier E (2010) Preference learning. Springer
Ahmadi Fahandar M, Hüllermeier E, Couso I (2017) Statistical inference for incomplete ranking data: the case of rank-dependent coarsening. In: Proceedings ICML–2017, 34th international conference on machine learning, Sydney, Australia
Denoeux T (2011) Maximum likelihood estimation from fuzzy data using the EM algorithm. Fuzzy Sets Syst 183(1):72–91
Denoeux T (2013) Maximum likelihood estimation from uncertain data in the belief function framework. IEEE Trans Knowl Data Eng 25(1):119–130
Hüllermeier E (2014) Learning from imprecise and fuzzy observations: data disambiguation through generalized loss minimization. Int J Approx Reason 55(7):1519–1534
Plass J, Cattaneo M, Schollmeyer G, Augustin T (2016) Testing of coarsening mechanism: coarsening at random versus subgroup independence. In: Proceedings of SMPS 2016, 8th international conference on soft methods in probability and statistics. Springer, pp 415–422
Viertl R (2011) Statistical methods for fuzzy data. Wiley
Couso I, Dubois D. A general framework for maximizing likelihood under incomplete data (Submitted for publication)
Dawid AP, Dickey JM (1977) Likelihood and bayesian inference from selectively reported data. J Am Stat Assoc 72:845–850
Jaeger M (2005) Ignorability for categorical data. Ann Stat 33(4):1964–1981
Bradley RA, Terry ME (1952) The rank analysis of incomplete block designs I. The method of paired comparisons. Biometrika 39:324–345
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Couso, I., Hüllermeier, E. (2018). Statistical Inference for Incomplete Ranking Data: A Comparison of Two Likelihood-Based Estimators. In: Mostaghim, S., Nürnberger, A., Borgelt, C. (eds) Frontiers in Computational Intelligence. Studies in Computational Intelligence, vol 739. Springer, Cham. https://doi.org/10.1007/978-3-319-67789-7_3
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DOI: https://doi.org/10.1007/978-3-319-67789-7_3
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