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

Cedric Archambeau, Fran├žois Caron
Multinomial logistic regression is one of the most popular models for modelling the ef- fect of explanatory variables on a subject choice between a set of speci ed 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 Metropolis- Hastings 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 in- troduction of a suitable set of auxiliary vari- ables leads to an Expectation-Maximization algorithm to nd Maximum A Posteriori es- timates of the parameters. We further pro- vide 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.
Conference on Uncertainty in Artificial Intelligence, Catalina Island, USA, August 15-17, 2012.