Abstract
Given a set of rating data for a set of items, determining the values of items is a matter of importance. Various probability models have been proposed to solve this task. The Plackett-Luce model is one of such models, which parametrizes the value of each item by a real valued preference parameter. In this paper, the Plackett-Luce model is generalized to cope with the grouped ranking observations such as movies or restaurants ratings. Since the maximization of the likelihood of the proposed model is computationally intractable, the lower bound of the likelihood which is easy to evaluate is derived, and the em algorithm is adopted to the maximization of the lower bound.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Terry, M., Bradley, R.A.: The rank analysis of incomplete block designs: I. the method of paired comparisons. Biometrika 39, 324–345 (1952)
Luce, R.D.: Individual Choice Behavior. John Wiley & Sons, Inc., New York (1959)
Plackett, R.L.: The analysis of permutations. Applied Statistics 24(2), 193–202 (1975)
Huang, T., Weng, R.C., Lin, C.: Generalized Bradley-Terry models and multi-class probability estimates. J. Mach. Learn. Res. 7, 85–115 (2006)
Hunter, D.R.: MM algorithms for generalized Bradley-Terry models. The Anaals of Statistics 32(1), 384–406 (2004)
Amari, S.: Information geometry of the EM and em algorithms for neural networks. Neural Networks 8(9), 1379–1408 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hino, H., Fujimoto, Y., Murata, N. (2009). Item Preference Parameters from Grouped Ranking Observations. In: Theeramunkong, T., Kijsirikul, B., Cercone, N., Ho, TB. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2009. Lecture Notes in Computer Science(), vol 5476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01307-2_91
Download citation
DOI: https://doi.org/10.1007/978-3-642-01307-2_91
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01306-5
Online ISBN: 978-3-642-01307-2
eBook Packages: Computer ScienceComputer Science (R0)