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Sampling and Learning Mallows and Generalized Mallows Models Under the Cayley Distance

Author

Listed:
  • Ekhine Irurozki

    (University of the Basque Country)

  • Borja Calvo

    (University of the Basque Country)

  • Jose A. Lozano

    (University of the Basque Country)

Abstract

The Mallows and Generalized Mallows models are compact yet powerful and natural ways of representing a probability distribution over the space of permutations. In this paper, we deal with the problems of sampling and learning such distributions when the metric on permutations is the Cayley distance. We propose new methods for both operations, and their performance is shown through several experiments. An application in the field of biology is given to motivate the interest of this model.

Suggested Citation

  • Ekhine Irurozki & Borja Calvo & Jose A. Lozano, 2018. "Sampling and Learning Mallows and Generalized Mallows Models Under the Cayley Distance," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 1-35, March.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:1:d:10.1007_s11009-016-9506-7
    DOI: 10.1007/s11009-016-9506-7
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    References listed on IDEAS

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    1. Jayanti Gupta & Paul Damien, 2002. "Conjugacy class prior distributions on metric‐based ranking models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 433-445, August.
    2. R. L. Plackett, 1975. "The Analysis of Permutations," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 24(2), pages 193-202, June.
    3. D'Elia, Angela & Piccolo, Domenico, 2005. "A mixture model for preferences data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 917-934, June.
    4. Murphy, Thomas Brendan & Martin, Donal, 2003. "Mixtures of distance-based models for ranking data," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 645-655, January.
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