## A hierarchical model for ordinal matrix factorization

Publication: Research - peer-review › Journal article – Annual report year: 2011

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**A hierarchical model for ordinal matrix factorization.** / Paquet, Ulrich; Thomson, Blaise; Winther, Ole.

Publication: Research - peer-review › Journal article – Annual report year: 2011

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*Statistics and Computing*, vol 22, no. 4, pp. 945-957., 10.1007/s11222-011-9264-x

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*Statistics and Computing*,

*22*(4), 945-957. 10.1007/s11222-011-9264-x

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*Statistics and Computing*. 2012, 22(4). 945-957. Available: 10.1007/s11222-011-9264-x

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TY - JOUR

T1 - A hierarchical model for ordinal matrix factorization

AU - Paquet,Ulrich

AU - Thomson,Blaise

AU - Winther,Ole

PB - Springer New York LLC

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Collaborative filtering

KW - Bayesian inference

KW - Ordinal regression

KW - Variational Bayes

KW - Low rank matrix decomposition

KW - Gibbs sampling

KW - Hierarchial modelling

KW - Large scale machine learning

U2 - 10.1007/s11222-011-9264-x

DO - 10.1007/s11222-011-9264-x

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 4

VL - 22

SP - 945

EP - 957

ER -