Modeling Events with Cascades of Poisson Processes

Aleksandr Simma, Michael Jordan
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:545-554, 2010.

Abstract

We present a probabilistic model of events in continuous time in which each event triggers a Poisson process of successor events. The ensemble of observed events is thereby modeled as a superposition of Poisson processes. Efficient inference is feasible under this model with an EM algorithm. Moreover, the EM algorithm can be implemented as a distributed algorithm, permitting the model to be applied to very large datasets. We apply these techniques to the modeling of Twitter messages and the revision history of Wikipedia.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR8-simma10a, title = {Modeling Events with Cascades of {P}oisson Processes}, author = {Simma, Aleksandr and Jordan, Michael}, booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence}, pages = {545--554}, year = {2010}, editor = {Grünwald, Peter and Spirtes, Peter}, volume = {R8}, series = {Proceedings of Machine Learning Research}, month = {08--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r8/main/assets/simma10a/simma10a.pdf}, url = {https://proceedings.mlr.press/r8/simma10a.html}, abstract = {We present a probabilistic model of events in continuous time in which each event triggers a Poisson process of successor events. The ensemble of observed events is thereby modeled as a superposition of Poisson processes. Efficient inference is feasible under this model with an EM algorithm. Moreover, the EM algorithm can be implemented as a distributed algorithm, permitting the model to be applied to very large datasets. We apply these techniques to the modeling of Twitter messages and the revision history of Wikipedia.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Modeling Events with Cascades of Poisson Processes %A Aleksandr Simma %A Michael Jordan %B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2010 %E Peter Grünwald %E Peter Spirtes %F pmlr-vR8-simma10a %I PMLR %P 545--554 %U https://proceedings.mlr.press/r8/simma10a.html %V R8 %X We present a probabilistic model of events in continuous time in which each event triggers a Poisson process of successor events. The ensemble of observed events is thereby modeled as a superposition of Poisson processes. Efficient inference is feasible under this model with an EM algorithm. Moreover, the EM algorithm can be implemented as a distributed algorithm, permitting the model to be applied to very large datasets. We apply these techniques to the modeling of Twitter messages and the revision history of Wikipedia. %Z Reissued by PMLR on 04 October 2026.
APA
Simma, A. & Jordan, M.. (2010). Modeling Events with Cascades of Poisson Processes. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:545-554 Available from https://proceedings.mlr.press/r8/simma10a.html. Reissued by PMLR on 04 October 2026.

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