Hawkesian Graphical Event Models

Xiufan Yu, Karthikeyan Shanmugam, Debarun Bhattacharjya, Tian Gao, Dharmashankar Subramanian, Lingzhou Xue
Proceedings of the 10th International Conference on Probabilistic Graphical Models, PMLR 138:569-580, 2020.

Abstract

Graphical event models (GEMs) provide a framework for graphical representation of multivariate point processes. We propose a class of GEMs named Hawkesian graphical event models (HGEMs) for representing temporal dependencies among different types of events from either a single event stream or multiple independent streams. In our proposed model, the intensity function for an event label is a linear combination of time-shifted kernels where time shifts correspond to prior occurrences of causal event labels in the history, as in a Hawkes process. The number of parameters in our model scales linearly in the number of edges in the graphical model, enabling efficient estimation and inference. This is in contrast to many existing GEMs where the number of parameters scales exponentially in the edges. We use two types of kernels: exponential and Gaussian kernels, and propose a two-step algorithm that combines the strengths of both kernels and learns the structure for the underlying graphical model. Experiments on both synthetic and real-world data demonstrate the efficacy of the proposed HGEM, and exhibit expressive power of the two-step learning algorithm in characterizing self-exciting event patterns and reflecting intrinsic Granger-causal relationships.

Cite this Paper

BibTeX
@InProceedings{pmlr-v138-yu20a, title = {Hawkesian Graphical Event Models}, author = {Yu, Xiufan and Shanmugam, Karthikeyan and Bhattacharjya, Debarun and Gao, Tian and Subramanian, Dharmashankar and Xue, Lingzhou}, booktitle = {Proceedings of the 10th International Conference on Probabilistic Graphical Models}, pages = {569--580}, year = {2020}, editor = {Jaeger, Manfred and Nielsen, Thomas Dyhre}, volume = {138}, series = {Proceedings of Machine Learning Research}, month = {23--25 Sep}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v138/yu20a/yu20a.pdf}, url = {https://proceedings.mlr.press/v138/yu20a.html}, abstract = {Graphical event models (GEMs) provide a framework for graphical representation of multivariate point processes. We propose a class of GEMs named Hawkesian graphical event models (HGEMs) for representing temporal dependencies among different types of events from either a single event stream or multiple independent streams. In our proposed model, the intensity function for an event label is a linear combination of time-shifted kernels where time shifts correspond to prior occurrences of causal event labels in the history, as in a Hawkes process. The number of parameters in our model scales linearly in the number of edges in the graphical model, enabling efficient estimation and inference. This is in contrast to many existing GEMs where the number of parameters scales exponentially in the edges. We use two types of kernels: exponential and Gaussian kernels, and propose a two-step algorithm that combines the strengths of both kernels and learns the structure for the underlying graphical model. Experiments on both synthetic and real-world data demonstrate the efficacy of the proposed HGEM, and exhibit expressive power of the two-step learning algorithm in characterizing self-exciting event patterns and reflecting intrinsic Granger-causal relationships.} }
Endnote
%0 Conference Paper %T Hawkesian Graphical Event Models %A Xiufan Yu %A Karthikeyan Shanmugam %A Debarun Bhattacharjya %A Tian Gao %A Dharmashankar Subramanian %A Lingzhou Xue %B Proceedings of the 10th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2020 %E Manfred Jaeger %E Thomas Dyhre Nielsen %F pmlr-v138-yu20a %I PMLR %P 569--580 %U https://proceedings.mlr.press/v138/yu20a.html %V 138 %X Graphical event models (GEMs) provide a framework for graphical representation of multivariate point processes. We propose a class of GEMs named Hawkesian graphical event models (HGEMs) for representing temporal dependencies among different types of events from either a single event stream or multiple independent streams. In our proposed model, the intensity function for an event label is a linear combination of time-shifted kernels where time shifts correspond to prior occurrences of causal event labels in the history, as in a Hawkes process. The number of parameters in our model scales linearly in the number of edges in the graphical model, enabling efficient estimation and inference. This is in contrast to many existing GEMs where the number of parameters scales exponentially in the edges. We use two types of kernels: exponential and Gaussian kernels, and propose a two-step algorithm that combines the strengths of both kernels and learns the structure for the underlying graphical model. Experiments on both synthetic and real-world data demonstrate the efficacy of the proposed HGEM, and exhibit expressive power of the two-step learning algorithm in characterizing self-exciting event patterns and reflecting intrinsic Granger-causal relationships.
APA
Yu, X., Shanmugam, K., Bhattacharjya, D., Gao, T., Subramanian, D. & Xue, L.. (2020). Hawkesian Graphical Event Models. Proceedings of the 10th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 138:569-580 Available from https://proceedings.mlr.press/v138/yu20a.html.

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