Abstract
We study the problem of constructing a probabilistic rating system for team competitions. Unlike previous studies, we consider a setting where the competition can be broken down into relatively small individual tasks, and it is reasonable to assume that each task is done by a single team member. We begin with a simplistic naïve Bayes approach which is this case reduces to logistic regression and then develop it into a more complex model with latent variables trained by expectation–maximization. We show experimental results that validate our approach.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Elo, A.: The Ratings of Chess Players: Past and Present. Arco, New York (1978)
Wu, T.F., Lin, C.J., Weng, R.C.: Probability estimates for multi-class classification by pairwise coupling. J. Mach. Learn. Res. 5, 975–1005 (2004)
Huang, T.K., Weng, R.C., Lin, C.J.: Generalized bradley-terry models and multi-class probability estimates. J. Mach. Learn. Res. 7, 85–115 (2006)
Stein, A., Aryal, J., Gort, G.: Generalized bradley-terry models and multi-class probability estimates. IEEE Trans. Geosci. Remote Sens. 43, 852–856 (2005)
Coulom, R.: Computing Elo ratings of move patterns in the game of Go. ICGA J. 30(4), 198–208 (2007)
Graepel, T., Candela, J.Q., Borchert, T., Herbrich, R.: Web-scale bayesian click-through rate prediction for sponsored search advertising in microsoft’s bing search engine. In: Proceedings of the \(27^{\text{ th }}\) International Conference on Machine Learning, pp. 13–20 (2010)
Graepel, T., Minka, T., Herbrich, R.: TrueSkill(tm): a bayesian skill rating system. In: Schölkopf, B., Platt, J., Hoffman, T. (eds.) Advances in Neural Information Processing Systems 19, pp. 569–576. MIT Press, Cambridge (2007)
Bradley, R.A., Terry, M.E.: Rank analysis of incomplete block designs. I. The method of paired comparisons. Biometrika 39, 324–245 (1952)
Agresti, A.: Categorical Data Analysis. Wiley, New York (1990)
Hunter, D.R.: MM algorithms for generalized bradley-terry models. Ann. Stat. 32(1), 384–406 (2004)
Plackett, R.L.: The analysis of permutations. J. Appl. Stat. 24, 193–202 (1975)
Marden, J.I.: Analyzing and Modeling Rank Data. Chapman and Hall, London (1995)
Menke, J.E., Martinez, T.R.: A bradley-terry artificial neural network model for individual ratings in group competitions. Neural Comput. Appl. 17(2), 175–186 (2008)
Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, New York (2006)
Nikolenko, S.I., Sirotkin, A.V.: A new bayesian rating system for team competitions. In: Proceedings of the \(28^{\text{ th }}\) International Conference on Machine Learning, pp. 601–608 (2011)
Nikolenko, S.I., Serdyuk, D.V., Sirotkin, A.V.: Bayesian rating systems with additional information on tournament results. SPIIRAS Proc. 22, 189–204 (2012)
Zhang, H.: The optimality of naive bayes. In: Barr, V., Markov, Z. (eds.) Proceedings of the Seventeenth International Florida Artificial Intelligence Research Society Conference (FLAIRS 2004). AAAI Press (2004)
Zhang, H., Su, J.: Naive bayesian classifiers for ranking. In: Boulicaut, J.-F., Esposito, F., Giannotti, F., Pedreschi, D. (eds.) ECML 2004. LNCS (LNAI), vol. 3201, pp. 501–512. Springer, Heidelberg (2004)
Ward, G., Hastie, T., Barry, S., Elith, J., Leathwick, J.R.: Presence-only data and the EM algorithm. Biometrics 65(2), 554–563 (2009)
Royle, J.A., Chandler, R.B., Yackulic, C., Nichols, J.D.: Likelihood analysis of species occurrence probability from presence-only data for modelling species distributions. Methods Ecol. Evol. 3(3), 545–554 (2012)
Divino, F., Golini, N., Lasinio, G.J., Penttinen, A.: Bayesian modeling and MCMC computation in linear logistic regression for presence-only data (2013). arXiv:1305.1232 [stat.CO]
Elkan, C., Noto, K.: Learning classifiers from only positive and unlabeled data. In: Proceedings of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD 2008, pp. 213–220. ACM, New York (2008)
Fawcett, T.: An introduction to ROC analysis. Pattern Recogn. Lett. 27(8), 861–874 (2006)
Ling, C.X., Huang, J., Zhang, H.: AUC: a statistically consistent and more discriminating measure than accuracy. Proc. Int. Joint Conf. Artif. Intel. 2003, 519–526 (2003)
Acknowledgements
This research has been partially supported by the Russian Foundation for Basic Research grant no. 15-29-01173, Government of the Russian Federation grant 14.Z50.31.0030, and the Presidential Grant for Leading Scientific Schools, NSh-3856.2014.1. I also thank Alexey Tugarev for providing access to the database of “What? Where? When?” tournament results.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Nikolenko, S. (2015). A Probabilistic Rating System for Team Competitions with Individual Contributions. In: Khachay, M., Konstantinova, N., Panchenko, A., Ignatov, D., Labunets, V. (eds) Analysis of Images, Social Networks and Texts. AIST 2015. Communications in Computer and Information Science, vol 542. Springer, Cham. https://doi.org/10.1007/978-3-319-26123-2_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-26123-2_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26122-5
Online ISBN: 978-3-319-26123-2
eBook Packages: Computer ScienceComputer Science (R0)