A Majorization-Minimization Algorithm for Nonnegative Binary Matrix Factorization
This paper tackles the problem of decomposing binary data using matrix factorization. We consider the family of mean-parametrized Bernoulli models, a class of generative models that are well suited for modeling binary data and enables interpretability of the factors. We factorize the Bernoulli param...
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| Vydáno v: | IEEE signal processing letters Ročník 29; s. 1526 - 1530 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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IEEE
01.01.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Institute of Electrical and Electronics Engineers |
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| ISSN: | 1070-9908, 1558-2361 |
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| Abstract | This paper tackles the problem of decomposing binary data using matrix factorization. We consider the family of mean-parametrized Bernoulli models, a class of generative models that are well suited for modeling binary data and enables interpretability of the factors. We factorize the Bernoulli parameter and consider an additional Beta prior on one of the factors to further improve the model's expressive power. While similar models have been proposed in the literature, they only exploit the Beta prior as a proxy to ensure a valid Bernoulli parameter in a Bayesian setting; in practice it reduces to a uniform or uninformative prior. Besides, estimation in these models has focused on costly Bayesian inference. In this paper, we propose a simple yet very efficient majorization-minimization algorithm for maximum a posteriori estimation. Our approach leverages the Beta prior whose parameters can be tuned to improve performance in matrix completion tasks. Experiments conducted on three public binary datasets show that our approach offers an excellent trade-off between prediction performance, computational complexity, and interpretability. |
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| AbstractList | This paper tackles the problem of decomposing binary data using matrix factorization. We consider the family of mean-parametrized Bernoulli models, a class of generative models that are well suited for modeling binary data and enables interpretability of the factors. We factorize the Bernoulli parameter and consider an additional Beta prior on one of the factors to further improve the model’s expressive power. While similar models have been proposed in the literature, they only exploit the Beta prior as a proxy to ensure a valid Bernoulli parameter in a Bayesian setting; in practice it reduces to a uniform or uninformative prior. Besides, estimation in these models has focused on costly Bayesian inference. In this paper, we propose a simple yet very efficient majorization-minimization algorithm for maximum a posteriori estimation. Our approach leverages the Beta prior whose parameters can be tuned to improve performance in matrix completion tasks. Experiments conducted on three public binary datasets show that our approach offers an excellent trade-off between prediction performance, computational complexity, and interpretability. |
| Author | Magron, Paul Fevotte, Cedric |
| Author_xml | – sequence: 1 givenname: Paul orcidid: 0000-0002-8561-0961 surname: Magron fullname: Magron, Paul email: paul.magron@inria.fr organization: CNRS, Inria, LORIA, Université de Lorraine, Nancy, France – sequence: 2 givenname: Cedric orcidid: 0000-0003-3801-5534 surname: Fevotte fullname: Fevotte, Cedric email: cedric.fevotte@irit.fr organization: IRIT, CNRS, Université de Toulouse, Toulouse, France |
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| Keywords | binary data mean-parametrized Bernoulli model majorization-minimization nonnegative matrix factorization |
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| SubjectTerms | Algorithms Bayesian analysis Binary data Biological system modeling Computational modeling Computer Science Data models Estimation Factorization Information Retrieval Logistics majorization-minimization Mathematical models mean-parametrized Bernoulli model nonnegative matrix factorization Optimization Parameters Performance enhancement Principal component analysis Statistical inference Upper bound |
| Title | A Majorization-Minimization Algorithm for Nonnegative Binary Matrix Factorization |
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