Plackett-Luce regression : A new Bayesian model for polychotomous data
Cedric Archambeau, François 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 specied 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.