A hierarchical model for ordinal matrix factorization

Ulrich Paquet, Blaise Thomson, Ole Winther

    Research output: Contribution to journalJournal articleResearchpeer-review


    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.
    Original languageEnglish
    JournalStatistics and Computing
    Issue number4
    Pages (from-to)945-957
    Publication statusPublished - 2012


    • Collaborative filtering
    • Bayesian inference
    • Ordinal regression
    • Variational Bayes
    • Low rank matrix decomposition
    • Gibbs sampling
    • Hierarchial modelling
    • Large scale machine learning


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