Stick-Breaking Beta Processes and the Poisson Process

John Paisley, David Blei, Michael Jordan
Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, PMLR 22:850-858, 2012.

Abstract

We show that the stick-breaking construction of the beta process due to \citePaisley:2010 can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying representation to derive error bounds on truncated beta processes that are tighter than those in the literature. We also develop a new MCMC inference algorithm for beta processes, based in part on our new Poisson process construction.

Cite this Paper

BibTeX
@InProceedings{pmlr-v22-paisley12, title = {Stick-Breaking Beta Processes and the Poisson Process}, author = {Paisley, John and Blei, David and Jordan, Michael}, booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics}, pages = {850--858}, year = {2012}, editor = {Lawrence, Neil D. and Girolami, Mark}, volume = {22}, series = {Proceedings of Machine Learning Research}, address = {La Palma, Canary Islands}, month = {21--23 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v22/paisley12/paisley12.pdf}, url = {https://proceedings.mlr.press/v22/paisley12.html}, abstract = {We show that the stick-breaking construction of the beta process due to \citePaisley:2010 can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying representation to derive error bounds on truncated beta processes that are tighter than those in the literature. We also develop a new MCMC inference algorithm for beta processes, based in part on our new Poisson process construction.} }
Endnote
%0 Conference Paper %T Stick-Breaking Beta Processes and the Poisson Process %A John Paisley %A David Blei %A Michael Jordan %B Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2012 %E Neil D. Lawrence %E Mark Girolami %F pmlr-v22-paisley12 %I PMLR %P 850--858 %U https://proceedings.mlr.press/v22/paisley12.html %V 22 %X We show that the stick-breaking construction of the beta process due to \citePaisley:2010 can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying representation to derive error bounds on truncated beta processes that are tighter than those in the literature. We also develop a new MCMC inference algorithm for beta processes, based in part on our new Poisson process construction.
RIS
TY - CPAPER TI - Stick-Breaking Beta Processes and the Poisson Process AU - John Paisley AU - David Blei AU - Michael Jordan BT - Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics DA - 2012/03/21 ED - Neil D. Lawrence ED - Mark Girolami ID - pmlr-v22-paisley12 PB - PMLR DP - Proceedings of Machine Learning Research VL - 22 SP - 850 EP - 858 L1 - http://proceedings.mlr.press/v22/paisley12/paisley12.pdf UR - https://proceedings.mlr.press/v22/paisley12.html AB - We show that the stick-breaking construction of the beta process due to \citePaisley:2010 can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying representation to derive error bounds on truncated beta processes that are tighter than those in the literature. We also develop a new MCMC inference algorithm for beta processes, based in part on our new Poisson process construction. ER -
APA
Paisley, J., Blei, D. & Jordan, M.. (2012). Stick-Breaking Beta Processes and the Poisson Process. Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 22:850-858 Available from https://proceedings.mlr.press/v22/paisley12.html.

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