Universal Models of Multivariate Temporal Point Processes

Asela Gunawardana, Chris Meek
Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, PMLR 51:556-563, 2016.

Abstract

With the rapidly increasing availability of event stream data there is growing interest in multivariate temporal point process models to capture both qualitative and quantitative features of this type of data. Recent research on multivariate point processes have focused in inference and estimation problems for restricted classes of models such as continuous time Bayesian networks, Markov jump processes, Gaussian Cox processes, and Hawkes Processes. In this paper, we study the expressive power and learnability of Graphical Event Models (GEMs) – the analogue of directed graphical models for multivariate temporal point processes. In particular, we describe a set of Graphical Event Models (GEMs) and show that this class can universally approximate any smooth multivariate temporal point process. We also describe a universal learning algorithm for this class of GEMs and show, under a mild set of assumptions, learnability results for both the dependency structures and distributions in this class. Our consistency results demonstrate the possibility of learning about both qualitative and quantitative dependencies from rich event stream data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v51-gunawardana16, title = {Universal Models of Multivariate Temporal Point Processes}, author = {Gunawardana, Asela and Meek, Chris}, booktitle = {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics}, pages = {556--563}, year = {2016}, editor = {Gretton, Arthur and Robert, Christian C.}, volume = {51}, series = {Proceedings of Machine Learning Research}, address = {Cadiz, Spain}, month = {09--11 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v51/gunawardana16.pdf}, url = {https://proceedings.mlr.press/v51/gunawardana16.html}, abstract = {With the rapidly increasing availability of event stream data there is growing interest in multivariate temporal point process models to capture both qualitative and quantitative features of this type of data. Recent research on multivariate point processes have focused in inference and estimation problems for restricted classes of models such as continuous time Bayesian networks, Markov jump processes, Gaussian Cox processes, and Hawkes Processes. In this paper, we study the expressive power and learnability of Graphical Event Models (GEMs) – the analogue of directed graphical models for multivariate temporal point processes. In particular, we describe a set of Graphical Event Models (GEMs) and show that this class can universally approximate any smooth multivariate temporal point process. We also describe a universal learning algorithm for this class of GEMs and show, under a mild set of assumptions, learnability results for both the dependency structures and distributions in this class. Our consistency results demonstrate the possibility of learning about both qualitative and quantitative dependencies from rich event stream data.} }
Endnote
%0 Conference Paper %T Universal Models of Multivariate Temporal Point Processes %A Asela Gunawardana %A Chris Meek %B Proceedings of the 19th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2016 %E Arthur Gretton %E Christian C. Robert %F pmlr-v51-gunawardana16 %I PMLR %P 556--563 %U https://proceedings.mlr.press/v51/gunawardana16.html %V 51 %X With the rapidly increasing availability of event stream data there is growing interest in multivariate temporal point process models to capture both qualitative and quantitative features of this type of data. Recent research on multivariate point processes have focused in inference and estimation problems for restricted classes of models such as continuous time Bayesian networks, Markov jump processes, Gaussian Cox processes, and Hawkes Processes. In this paper, we study the expressive power and learnability of Graphical Event Models (GEMs) – the analogue of directed graphical models for multivariate temporal point processes. In particular, we describe a set of Graphical Event Models (GEMs) and show that this class can universally approximate any smooth multivariate temporal point process. We also describe a universal learning algorithm for this class of GEMs and show, under a mild set of assumptions, learnability results for both the dependency structures and distributions in this class. Our consistency results demonstrate the possibility of learning about both qualitative and quantitative dependencies from rich event stream data.
RIS
TY - CPAPER TI - Universal Models of Multivariate Temporal Point Processes AU - Asela Gunawardana AU - Chris Meek BT - Proceedings of the 19th International Conference on Artificial Intelligence and Statistics DA - 2016/05/02 ED - Arthur Gretton ED - Christian C. Robert ID - pmlr-v51-gunawardana16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 51 SP - 556 EP - 563 L1 - http://proceedings.mlr.press/v51/gunawardana16.pdf UR - https://proceedings.mlr.press/v51/gunawardana16.html AB - With the rapidly increasing availability of event stream data there is growing interest in multivariate temporal point process models to capture both qualitative and quantitative features of this type of data. Recent research on multivariate point processes have focused in inference and estimation problems for restricted classes of models such as continuous time Bayesian networks, Markov jump processes, Gaussian Cox processes, and Hawkes Processes. In this paper, we study the expressive power and learnability of Graphical Event Models (GEMs) – the analogue of directed graphical models for multivariate temporal point processes. In particular, we describe a set of Graphical Event Models (GEMs) and show that this class can universally approximate any smooth multivariate temporal point process. We also describe a universal learning algorithm for this class of GEMs and show, under a mild set of assumptions, learnability results for both the dependency structures and distributions in this class. Our consistency results demonstrate the possibility of learning about both qualitative and quantitative dependencies from rich event stream data. ER -
APA
Gunawardana, A. & Meek, C.. (2016). Universal Models of Multivariate Temporal Point Processes. Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 51:556-563 Available from https://proceedings.mlr.press/v51/gunawardana16.html.

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