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hal-00755478, version 1

Bayesian nonparametric Plackett-Luce models for the analysis of clustered ranked data

Francois Caron (, http://www.math.u-bordeaux1.fr/~fcaron/) a12, Yee Whye Teh (http://www.stats.ox.ac.uk/~teh/) b3, Thomas Brendan Murphy c4

N° RR-8143 (2012)

Abstract: In this paper we propose a Bayesian nonparametric model for clustering partial ranking data. We start by developing a Bayesian nonparametric extension of the popular Plackett-Luce choice model that can handle an infinite number of choice items. Our framework is based on the theory of random atomic measures, with prior specified by a completely random measure. We characterise the posterior distribution given data, and derive a simple and effective Gibbs sampler for posterior simulation. We then develop a Dirichlet process mixture extension of our model and apply it to clustering the preferences for university programmes of Irish secondary school graduates.

  • a –  INRIA
  • b –  Oxford University
  • c –  University College Dublin
  • 1:  ALEA (INRIA Bordeaux - Sud-Ouest)
  • INRIA – Université de Bordeaux – CNRS : UMR5251
  • 2:  Institut de Mathématiques de Bordeaux (IMB)
  • CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
  • 3:  Department of Statistics [Oxford]
  • University of Oxford
  • 4:  School of Mathematical Sciences
  • University College Dublin
  • Domain : Statistics/Machine Learning
    Statistics/Methodology
    Statistics/Applications
  • Keywords : choice models – generalized Bradley-Terry model – Plackett-Luce model – completely random measure – Mixture model – Dirichlet process – Markov Chain Monte Carlo
  • Internal note : RR-8143
  • Available versions :  v1 (2012-11-21) v2 (2014-01-14)
 
  • hal-00755478, version 1
  • oai:hal.inria.fr:hal-00755478
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  • Submitted on: Wednesday, 21 November 2012 13:34:00
  • Updated on: Wednesday, 21 November 2012 15:10:01