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
Hlavní autoři: Magron, Paul, Fevotte, Cedric
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York 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.
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
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  organization: IRIT, CNRS, Université de Toulouse, Toulouse, France
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10.1038/s42254-020-00275-1
10.1016/j.neucom.2007.07.038
10.1109/TPAMI.2017.2651816
10.1007/s11045-013-0240-9
10.1198/0003130042836
10.1038/44565
10.1162/NECO_a_00168
10.1016/j.jmva.2020.104668
10.1109/TSP.2016.2601299
10.1109/ICDM.2008.22
10.1111/1467-9868.00196
10.5555/2981562.2981720
10.1016/j.ins.2020.12.001
10.1109/WASPAA.2017.8170035
10.1007/978-1-4899-7637-6_13
10.1109/MC.2009.263
10.4324/9780203405345-14
10.1007/s10618-020-00712-w
10.7551/mitpress/1120.003.0084
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mean-parametrized Bernoulli model
majorization-minimization
nonnegative matrix factorization
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References ref13
ref12
ref14
ref11
ref10
ref2
ref1
ref17
ref19
Gopalan (ref8) 2014
Kemp (ref27) 2006
ref24
ref23
ref26
ref25
ref22
Hofmann (ref29) 1999
ref21
Tipping (ref16) 1998
Larsen (ref20) 2015
ref7
Bertin-Mahieux (ref28) 2011
Zhou (ref15) 2015
ref4
ref3
ref6
Gopalan (ref9) 2014
ref5
Schein (ref18) 2003
References_xml – ident: ref1
  doi: 10.1007/s10044-007-0096-4
– ident: ref23
  doi: 10.1038/s42254-020-00275-1
– ident: ref4
  doi: 10.1016/j.neucom.2007.07.038
– ident: ref26
  doi: 10.1109/TPAMI.2017.2651816
– start-page: 592
  volume-title: Proc. Int. Conf. Neural Inf. Process. Syst.
  year: 1998
  ident: ref16
  article-title: Probabilistic visualisation of high-dimensional binary data
– start-page: 240
  volume-title: Proc. 9th Int. Workshop Artif. Intell. Statist.
  year: 2003
  ident: ref18
  article-title: A generalized linear model for principal component analysis of binary data
– ident: ref19
  doi: 10.1007/s11045-013-0240-9
– ident: ref13
  doi: 10.1198/0003130042836
– ident: ref6
  doi: 10.1038/44565
– ident: ref24
  doi: 10.1162/NECO_a_00168
– ident: ref11
  doi: 10.1016/j.jmva.2020.104668
– start-page: 50
  volume-title: Proc. 15th Conf. Uncertainty Artif. Intell.
  year: 1999
  ident: ref29
  article-title: Probabilistic latent semantic analysis
– ident: ref14
  doi: 10.1109/TSP.2016.2601299
– ident: ref10
  doi: 10.1109/ICDM.2008.22
– ident: ref21
  doi: 10.1111/1467-9868.00196
– ident: ref7
  doi: 10.5555/2981562.2981720
– ident: ref22
  doi: 10.1016/j.ins.2020.12.001
– ident: ref25
  doi: 10.1109/WASPAA.2017.8170035
– ident: ref3
  doi: 10.1007/978-1-4899-7637-6_13
– start-page: 3176
  volume-title: Proc. 27th Int. Conf. Neural Inf. Process. Syst.
  year: 2014
  ident: ref8
  article-title: Content-based recommendations with poisson factorization
– ident: ref5
  doi: 10.1109/MC.2009.263
– start-page: 1135
  volume-title: Proc. Int. Conf. Artif. Intell. Statist.
  year: 2015
  ident: ref15
  article-title: Infinite edge partition models for overlapping community detection and link prediction
– start-page: 591
  volume-title: Proc. 12th Int. Conf. Music Inf. Retrieval
  year: 2011
  ident: ref28
  article-title: The million song dataset
– ident: ref2
  doi: 10.4324/9780203405345-14
– start-page: 381
  volume-title: Proc. 21st Nat. Conf. Artif. Intell.
  year: 2006
  ident: ref27
  article-title: Learning systems of concepts with an infinite relational model
– ident: ref12
  doi: 10.1007/s10618-020-00712-w
– start-page: 326
  volume-title: Proc. 31st Conf. Uncertainty Artif. Intell.
  year: 2014
  ident: ref9
  article-title: Scalable recommendation with hierarchical poisson factorization
– start-page: 555
  volume-title: Proc. Int. Joint Conf. Knowl. Discov., Knowl. Eng. Knowl. Manage.
  year: 2015
  ident: ref20
  article-title: Non-negative matrix factorization for binary data
– ident: ref17
  doi: 10.7551/mitpress/1120.003.0084
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Snippet This paper tackles the problem of decomposing binary data using matrix factorization. We consider the family of mean-parametrized Bernoulli models, a class of...
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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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