Hierarchical Model for Ordinal Matrix Factorization
Ulrich Paquet, Blaise Thomson and Ole Winther
Statistics and Computing
This paper proposes a hierarchical probabilistic model for ordinal matrix factorization.
Unlike previous approaches, we model the ordinal nature of the data and take a principled
approach to incorporating priors for the hidden variables. Two algorithms are presented for
inference, one based on Gibbs sampling and one based on variational Bayes. Importantly,
these algorithms may be implemented in the factorization of very large matrices with
missing entries. The model is evaluated on a collaborative filtering task, where users have
rated a collection of movies and the system is asked to predict their ratings for other
movies. The Netflix data set is used for evaluation, which consists of around 100 million
ratings. Using root mean-squared error (RMSE) as an evaluation metric, results show that
the suggested model outperforms alternative factorization techniques. Results also show
how Gibbs sampling outperforms variational Bayes on this task, despite the large number
of ratings and model parameters. Matlab implementations of the proposed algorithms are
available from cogsys.imm.dtu.dk/ordinalmatrixfactorization.