CUED Publications database

A Hierarchical Model for Ordinal Matrix Factorization

Paquet, U and Thomson, BRM and Winther, O (2012) A Hierarchical Model for Ordinal Matrix Factorization. Statistics and Computing, 22. pp. 945-957. ISSN 0960-3174

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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

Item Type: Article
Divisions: Div F > Machine Intelligence
Depositing User: Cron Job
Date Deposited: 09 Dec 2016 18:48
Last Modified: 27 Apr 2017 10:03