Bayesian learning of joint distributions of objects

Anjishnu Banerjee, Jared Murray, David Dunson
Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, PMLR 31:1-9, 2013.

Abstract

There is increasing interest in broad application areas in defining flexible joint models for data having a variety of measurement scales, while also allowing data of complex types, such as functions, images and documents. We consider a general framework for nonparametric Bayes joint modeling through mixture models that incorporate dependence across data types through a joint mixing measure. The mixing measure is assigned a novel infinite tensor factorization (ITF) prior that allows flexible dependence in cluster allocation across data types. The ITF prior is formulated as a tensor product of stick-breaking processes. Focusing on a convenient special case corresponding to a Parafac factorization, we provide basic theory justifying the flexibility of the proposed prior. Focusing on ITF mixtures of product kernels, we develop a new Gibbs sampling algorithm for routine implementation relying on slice sampling. The methods are compared with alternative joint mixture models based on Dirichlet processes and related approaches through simulations and real data applications.

Cite this Paper

BibTeX
@InProceedings{pmlr-v31-banerjee13a, title = {Bayesian learning of joint distributions of objects}, author = {Banerjee, Anjishnu and Murray, Jared and Dunson, David}, booktitle = {Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics}, pages = {1--9}, year = {2013}, editor = {Carvalho, Carlos M. and Ravikumar, Pradeep}, volume = {31}, series = {Proceedings of Machine Learning Research}, address = {Scottsdale, Arizona, USA}, month = {29 Apr--01 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v31/banerjee13a.pdf}, url = {https://proceedings.mlr.press/v31/banerjee13a.html}, abstract = {There is increasing interest in broad application areas in defining flexible joint models for data having a variety of measurement scales, while also allowing data of complex types, such as functions, images and documents. We consider a general framework for nonparametric Bayes joint modeling through mixture models that incorporate dependence across data types through a joint mixing measure. The mixing measure is assigned a novel infinite tensor factorization (ITF) prior that allows flexible dependence in cluster allocation across data types. The ITF prior is formulated as a tensor product of stick-breaking processes. Focusing on a convenient special case corresponding to a Parafac factorization, we provide basic theory justifying the flexibility of the proposed prior. Focusing on ITF mixtures of product kernels, we develop a new Gibbs sampling algorithm for routine implementation relying on slice sampling. The methods are compared with alternative joint mixture models based on Dirichlet processes and related approaches through simulations and real data applications.}, note = {Notable paper award} }
Endnote
%0 Conference Paper %T Bayesian learning of joint distributions of objects %A Anjishnu Banerjee %A Jared Murray %A David Dunson %B Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2013 %E Carlos M. Carvalho %E Pradeep Ravikumar %F pmlr-v31-banerjee13a %I PMLR %P 1--9 %U https://proceedings.mlr.press/v31/banerjee13a.html %V 31 %X There is increasing interest in broad application areas in defining flexible joint models for data having a variety of measurement scales, while also allowing data of complex types, such as functions, images and documents. We consider a general framework for nonparametric Bayes joint modeling through mixture models that incorporate dependence across data types through a joint mixing measure. The mixing measure is assigned a novel infinite tensor factorization (ITF) prior that allows flexible dependence in cluster allocation across data types. The ITF prior is formulated as a tensor product of stick-breaking processes. Focusing on a convenient special case corresponding to a Parafac factorization, we provide basic theory justifying the flexibility of the proposed prior. Focusing on ITF mixtures of product kernels, we develop a new Gibbs sampling algorithm for routine implementation relying on slice sampling. The methods are compared with alternative joint mixture models based on Dirichlet processes and related approaches through simulations and real data applications. %Z Notable paper award
RIS
TY - CPAPER TI - Bayesian learning of joint distributions of objects AU - Anjishnu Banerjee AU - Jared Murray AU - David Dunson BT - Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics DA - 2013/04/29 ED - Carlos M. Carvalho ED - Pradeep Ravikumar ID - pmlr-v31-banerjee13a PB - PMLR DP - Proceedings of Machine Learning Research VL - 31 SP - 1 EP - 9 L1 - http://proceedings.mlr.press/v31/banerjee13a.pdf UR - https://proceedings.mlr.press/v31/banerjee13a.html AB - There is increasing interest in broad application areas in defining flexible joint models for data having a variety of measurement scales, while also allowing data of complex types, such as functions, images and documents. We consider a general framework for nonparametric Bayes joint modeling through mixture models that incorporate dependence across data types through a joint mixing measure. The mixing measure is assigned a novel infinite tensor factorization (ITF) prior that allows flexible dependence in cluster allocation across data types. The ITF prior is formulated as a tensor product of stick-breaking processes. Focusing on a convenient special case corresponding to a Parafac factorization, we provide basic theory justifying the flexibility of the proposed prior. Focusing on ITF mixtures of product kernels, we develop a new Gibbs sampling algorithm for routine implementation relying on slice sampling. The methods are compared with alternative joint mixture models based on Dirichlet processes and related approaches through simulations and real data applications. N1 - Notable paper award ER -
APA
Banerjee, A., Murray, J. & Dunson, D.. (2013). Bayesian learning of joint distributions of objects. Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 31:1-9 Available from https://proceedings.mlr.press/v31/banerjee13a.html. Notable paper award

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