Markov Beta Processes for Time Evolving Dictionary Learning

Amar Shah, Zoubin Ghahramani
Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, PMLR R14:356-365, 2016.

Abstract

We develop Markov beta processes (MBP) asa model suitable for data which can be representedby a sparse set of latent featureswhich evolve over time. Most time evolvingnonparametric latent feature models inthe literature vary feature usage, but maintaina constant set of features over time. Weshow that being able to model features whichthemselves evolve over time results in theMBP outperforming other beta process basedmodels. Our construction utilizes Poissonprocess operations, which leave each transformedbeta process marginally beta processdistributed. This allows one to analyticallymarginalize out latent beta processes, exploitingconjugacy when we couple them withBernoulli processes, leading to a surprisinglyelegant Gibbs MCMC scheme considering theexpressiveness of the prior. We apply themodel to the task of denoising and interpolatingnoisy image sequences and in predictingtime evolving gene expression data, demonstratingsuperior performance to other betaprocess based methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR14-shah16a, title = {{M}arkov Beta Processes for Time Evolving Dictionary Learning}, author = {Shah, Amar and Ghahramani, Zoubin}, booktitle = {Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence}, pages = {356--365}, year = {2016}, editor = {Ihler, Alexander and Janzing, Dominik}, volume = {R14}, series = {Proceedings of Machine Learning Research}, month = {25--29 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r14/main/assets/shah16a/shah16a.pdf}, url = {https://proceedings.mlr.press/r14/shah16a.html}, abstract = {We develop Markov beta processes (MBP) asa model suitable for data which can be representedby a sparse set of latent featureswhich evolve over time. Most time evolvingnonparametric latent feature models inthe literature vary feature usage, but maintaina constant set of features over time. Weshow that being able to model features whichthemselves evolve over time results in theMBP outperforming other beta process basedmodels. Our construction utilizes Poissonprocess operations, which leave each transformedbeta process marginally beta processdistributed. This allows one to analyticallymarginalize out latent beta processes, exploitingconjugacy when we couple them withBernoulli processes, leading to a surprisinglyelegant Gibbs MCMC scheme considering theexpressiveness of the prior. We apply themodel to the task of denoising and interpolatingnoisy image sequences and in predictingtime evolving gene expression data, demonstratingsuperior performance to other betaprocess based methods.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Markov Beta Processes for Time Evolving Dictionary Learning %A Amar Shah %A Zoubin Ghahramani %B Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2016 %E Alexander Ihler %E Dominik Janzing %F pmlr-vR14-shah16a %I PMLR %P 356--365 %U https://proceedings.mlr.press/r14/shah16a.html %V R14 %X We develop Markov beta processes (MBP) asa model suitable for data which can be representedby a sparse set of latent featureswhich evolve over time. Most time evolvingnonparametric latent feature models inthe literature vary feature usage, but maintaina constant set of features over time. Weshow that being able to model features whichthemselves evolve over time results in theMBP outperforming other beta process basedmodels. Our construction utilizes Poissonprocess operations, which leave each transformedbeta process marginally beta processdistributed. This allows one to analyticallymarginalize out latent beta processes, exploitingconjugacy when we couple them withBernoulli processes, leading to a surprisinglyelegant Gibbs MCMC scheme considering theexpressiveness of the prior. We apply themodel to the task of denoising and interpolatingnoisy image sequences and in predictingtime evolving gene expression data, demonstratingsuperior performance to other betaprocess based methods. %Z Reissued by PMLR on 04 October 2026.
APA
Shah, A. & Ghahramani, Z.. (2016). Markov Beta Processes for Time Evolving Dictionary Learning. Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R14:356-365 Available from https://proceedings.mlr.press/r14/shah16a.html. Reissued by PMLR on 04 October 2026.

Related Material