Uncertainty in Artificial Intelligence
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Plackett-Luce regression: A new Bayesian model for polychotomous data
Cedric Archambeau, Francois Caron
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.
Keywords:
Pages: 84-92
PS Link:
PDF Link: /papers/12/p84-archambeau.pdf
BibTex:
@INPROCEEDINGS{Archambeau12,
AUTHOR = "Cedric Archambeau and Francois Caron",
TITLE = "Plackett-Luce regression: A new Bayesian model for polychotomous data",
BOOKTITLE = "Proceedings of the Twenty-Eighth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-12)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2012",
PAGES = "84--92"
}


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