Plackett-Luce regression: A new Bayesian model for polychotomous data

Cedric Archambeau, Francois Caron
Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, PMLR R10:81-89, 2012.

Abstract

Multinomial logistic regression is one of the most popular models for modelling the effect of explanatory variables on a subject choice between a set of specified options. This model has found numerous applications in machine learning, psychology or economy. Bayesian inference in this model is non trivial and requires, either to resort to a MetropolisHastings algorithm, or rejection sampling within a Gibbs sampler. In this paper, we propose an alternative model to multinomial logistic regression. The model builds on the Plackett-Luce model, a popular model for multiple comparisons. We show that the introduction of a suitable set of auxiliary variables leads to an Expectation-Maximization algorithm to find Maximum A Posteriori estimates of the parameters. We further provide a full Bayesian treatment by deriving a Gibbs sampler, which only requires to sample from highly standard distributions. We also propose a variational approximate inference scheme. All are very simple to implement. One property of our Plackett-Luce regression model is that it learns a sparse set of feature weights. We compare our method to sparse Bayesian multinomial logistic regression and show that it is competitive, especially in presence of polychotomous data.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR10-archambeau12a, title = {Plackett-Luce regression: A new {B}ayesian model for polychotomous data}, author = {Archambeau, Cedric and Caron, Francois}, booktitle = {Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence}, pages = {81--89}, year = {2012}, editor = {de Freitas, Nando and Murphy, Kevin}, volume = {R10}, series = {Proceedings of Machine Learning Research}, month = {14--18 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r10/main/assets/archambeau12a/archambeau12a.pdf}, url = {https://proceedings.mlr.press/r10/archambeau12a.html}, abstract = {Multinomial logistic regression is one of the most popular models for modelling the effect of explanatory variables on a subject choice between a set of specified options. This model has found numerous applications in machine learning, psychology or economy. Bayesian inference in this model is non trivial and requires, either to resort to a MetropolisHastings algorithm, or rejection sampling within a Gibbs sampler. In this paper, we propose an alternative model to multinomial logistic regression. The model builds on the Plackett-Luce model, a popular model for multiple comparisons. We show that the introduction of a suitable set of auxiliary variables leads to an Expectation-Maximization algorithm to find Maximum A Posteriori estimates of the parameters. We further provide a full Bayesian treatment by deriving a Gibbs sampler, which only requires to sample from highly standard distributions. We also propose a variational approximate inference scheme. All are very simple to implement. One property of our Plackett-Luce regression model is that it learns a sparse set of feature weights. We compare our method to sparse Bayesian multinomial logistic regression and show that it is competitive, especially in presence of polychotomous data.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Plackett-Luce regression: A new Bayesian model for polychotomous data %A Cedric Archambeau %A Francois Caron %B Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2012 %E Nando de Freitas %E Kevin Murphy %F pmlr-vR10-archambeau12a %I PMLR %P 81--89 %U https://proceedings.mlr.press/r10/archambeau12a.html %V R10 %X Multinomial logistic regression is one of the most popular models for modelling the effect of explanatory variables on a subject choice between a set of specified options. This model has found numerous applications in machine learning, psychology or economy. Bayesian inference in this model is non trivial and requires, either to resort to a MetropolisHastings algorithm, or rejection sampling within a Gibbs sampler. In this paper, we propose an alternative model to multinomial logistic regression. The model builds on the Plackett-Luce model, a popular model for multiple comparisons. We show that the introduction of a suitable set of auxiliary variables leads to an Expectation-Maximization algorithm to find Maximum A Posteriori estimates of the parameters. We further provide a full Bayesian treatment by deriving a Gibbs sampler, which only requires to sample from highly standard distributions. We also propose a variational approximate inference scheme. All are very simple to implement. One property of our Plackett-Luce regression model is that it learns a sparse set of feature weights. We compare our method to sparse Bayesian multinomial logistic regression and show that it is competitive, especially in presence of polychotomous data. %Z Reissued by PMLR on 04 October 2026.
APA
Archambeau, C. & Caron, F.. (2012). Plackett-Luce regression: A new Bayesian model for polychotomous data. Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R10:81-89 Available from https://proceedings.mlr.press/r10/archambeau12a.html. Reissued by PMLR on 04 October 2026.

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