jmlr jmlr2008 jmlr2008-69 jmlr2008-69-reference knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Guy Lebanon, Yi Mao
Abstract: Statistical models on full and partial rankings of n items are often of limited practical use for large n due to computational consideration. We explore the use of non-parametric models for partially ranked data and derive computationally efficient procedures for their use for large n. The derivations are largely possible through combinatorial and algebraic manipulations based on the lattice of partial rankings. A bias-variance analysis and an experimental study demonstrate the applicability of the proposed method. Keywords: ranked data, partially ordered sets, kernel smoothing
W. S. Cleveland. The Elements of Graphing Data. Wadsworth Publ. Co., 1985. D. E. Critchlow. Metric Methods for Analyzing Partially Ranked Data. Lecture Notes in Statistics, volume 34, Springer, 1985. P. Diaconis. Group Representations in Probability and Statistics, volume 11 of IMS Lecture Notes – Monograph Series. Institute of Mathematical Statistics, 1988. P. Diaconis. A generalization of spectral analysis with application to ranked data. Annals of Statistics, 17(3):949–979, 1989. M. A. Fligner and J. S. Verducci. Distance based ranking models. Journal of the Royal Statistical Society B, 43:359–369, 1986. M. A. Fligner and J. S. Verducci. Multistage ranking models. Journal of the American Statistical Association, 83:892–901, 1988. 2428 N ON -PARAMETRIC M ODELING OF PARTIALLY R ANKED DATA M. A. Fligner and J. S. Verducci, editors. Probability Models and Statistical Analyses for Ranking Data. Springer-Verlag, 1993. J. Huang, C. Guestrin, and L. Guibas. Efficient inference for distributions on permutations. In Advances in Neural Information Processing Systems 20, pages 697–704. 2008. M. G. Kendall. A new measure of rank correlation. Biometrika, 30, 1938. R. Kondor, A. Howard, and T. Jebara. Multi-object tracking with representations of the symmetric group. In Artificial Intelligence and Statistics, 2007. G. Lebanon and J. Lafferty. Conditional models on the ranking poset. In Advances in Neural Information Processing Systems, 15, 2003. C. L. Mallows. Non-null ranking models. Biometrika, 44:114–130, 1957. J. I. Marden. Analyzing and Modeling Rank Data. CRC Press, 1996. P. Resnick, N. Iacovou, M. Suchak, P. Bergstrom, and J. Riedl. Grouplens: an open architecture for collaborative filtering of netnews. In Proceedings of the Conference on Computer Supported Cooperative Work, 1994. R. P. Stanley. Enumerative Combinatorics, volume 1. Cambridge University Press, 2000. G. L. Thompson. Generalized permutation polytopes and exploratory graphical methods for ranked data. The Annals of Statistics, 21(3):1401–1430, 1993. M. P. Wand and M. C. Jones. Kernel Smoothing. Chapman and Hall/CRC, 1995. 2429