Nonparametric Bayesian Factor Analysis for Dynamic Count Matrices

Ayan Acharya, Joydeep Ghosh, Mingyuan Zhou
Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, PMLR 38:1-9, 2015.

Abstract

A gamma process dynamic Poisson factor analysis model is proposed to factorize a dynamic count matrix, whose columns are sequentially observed count vectors. The model builds a novel Markov chain that sends the latent gamma random variables at time (t-1) as the shape parameters of those at time t, which are linked to observed or latent counts under the Poisson likelihood. The significant challenge of inferring the gamma shape parameters is fully addressed, using unique data augmentation and marginalization techniques for the negative binomial distribution. The same nonparametric Bayesian model also applies to the factorization of a dynamic binary matrix, via a Bernoulli-Poisson link that connects a binary observation to a latent count, with closed-form conditional posteriors for the latent counts and efficient computation for sparse observations. We apply the model to text and music analysis, with state-of-the-art results.

Cite this Paper

BibTeX
@InProceedings{pmlr-v38-acharya15, title = {{Nonparametric Bayesian Factor Analysis for Dynamic Count Matrices}}, author = {Acharya, Ayan and Ghosh, Joydeep and Zhou, Mingyuan}, booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics}, pages = {1--9}, year = {2015}, editor = {Lebanon, Guy and Vishwanathan, S. V. N.}, volume = {38}, series = {Proceedings of Machine Learning Research}, address = {San Diego, California, USA}, month = {09--12 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v38/acharya15.pdf}, url = {https://proceedings.mlr.press/v38/acharya15.html}, abstract = {A gamma process dynamic Poisson factor analysis model is proposed to factorize a dynamic count matrix, whose columns are sequentially observed count vectors. The model builds a novel Markov chain that sends the latent gamma random variables at time (t-1) as the shape parameters of those at time t, which are linked to observed or latent counts under the Poisson likelihood. The significant challenge of inferring the gamma shape parameters is fully addressed, using unique data augmentation and marginalization techniques for the negative binomial distribution. The same nonparametric Bayesian model also applies to the factorization of a dynamic binary matrix, via a Bernoulli-Poisson link that connects a binary observation to a latent count, with closed-form conditional posteriors for the latent counts and efficient computation for sparse observations. We apply the model to text and music analysis, with state-of-the-art results.} }
Endnote
%0 Conference Paper %T Nonparametric Bayesian Factor Analysis for Dynamic Count Matrices %A Ayan Acharya %A Joydeep Ghosh %A Mingyuan Zhou %B Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2015 %E Guy Lebanon %E S. V. N. Vishwanathan %F pmlr-v38-acharya15 %I PMLR %P 1--9 %U https://proceedings.mlr.press/v38/acharya15.html %V 38 %X A gamma process dynamic Poisson factor analysis model is proposed to factorize a dynamic count matrix, whose columns are sequentially observed count vectors. The model builds a novel Markov chain that sends the latent gamma random variables at time (t-1) as the shape parameters of those at time t, which are linked to observed or latent counts under the Poisson likelihood. The significant challenge of inferring the gamma shape parameters is fully addressed, using unique data augmentation and marginalization techniques for the negative binomial distribution. The same nonparametric Bayesian model also applies to the factorization of a dynamic binary matrix, via a Bernoulli-Poisson link that connects a binary observation to a latent count, with closed-form conditional posteriors for the latent counts and efficient computation for sparse observations. We apply the model to text and music analysis, with state-of-the-art results.
RIS
TY - CPAPER TI - Nonparametric Bayesian Factor Analysis for Dynamic Count Matrices AU - Ayan Acharya AU - Joydeep Ghosh AU - Mingyuan Zhou BT - Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics DA - 2015/02/21 ED - Guy Lebanon ED - S. V. N. Vishwanathan ID - pmlr-v38-acharya15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 38 SP - 1 EP - 9 L1 - http://proceedings.mlr.press/v38/acharya15.pdf UR - https://proceedings.mlr.press/v38/acharya15.html AB - A gamma process dynamic Poisson factor analysis model is proposed to factorize a dynamic count matrix, whose columns are sequentially observed count vectors. The model builds a novel Markov chain that sends the latent gamma random variables at time (t-1) as the shape parameters of those at time t, which are linked to observed or latent counts under the Poisson likelihood. The significant challenge of inferring the gamma shape parameters is fully addressed, using unique data augmentation and marginalization techniques for the negative binomial distribution. The same nonparametric Bayesian model also applies to the factorization of a dynamic binary matrix, via a Bernoulli-Poisson link that connects a binary observation to a latent count, with closed-form conditional posteriors for the latent counts and efficient computation for sparse observations. We apply the model to text and music analysis, with state-of-the-art results. ER -
APA
Acharya, A., Ghosh, J. & Zhou, M.. (2015). Nonparametric Bayesian Factor Analysis for Dynamic Count Matrices. Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 38:1-9 Available from https://proceedings.mlr.press/v38/acharya15.html.

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