  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.
