Learning Granger Causality for Hawkes Processes

Hongteng Xu, Mehrdad Farajtabar, Hongyuan Zha
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:1717-1726, 2016.

Abstract

Learning Granger causality for general point processes is a very challenging task. We propose an effective method learning Granger causality for a special but significant type of point processes — Hawkes processes. Focusing on Hawkes processes, we reveal the relationship between Hawkes process’s impact functions and its Granger causality graph. Specifically, our model represents impact functions using a series of basis functions and recovers the Granger causality graph via group sparsity of the impact functions’ coefficients. We propose an effective learning algorithm combining a maximum likelihood estimator (MLE) with a sparse-group-lasso (SGL) regularizer. Additionally, the pairwise similarity between the dimensions of the process is considered when their clustering structure is available. We analyze our learning method and discuss the selection of the basis functions. Experiments on synthetic data and real-world data show that our method can learn the Granger causality graph and the triggering patterns of Hawkes processes simultaneously.

Cite this Paper

BibTeX
@InProceedings{pmlr-v48-xuc16, title = {Learning Granger Causality for Hawkes Processes}, author = {Xu, Hongteng and Farajtabar, Mehrdad and Zha, Hongyuan}, booktitle = {Proceedings of The 33rd International Conference on Machine Learning}, pages = {1717--1726}, year = {2016}, editor = {Balcan, Maria Florina and Weinberger, Kilian Q.}, volume = {48}, series = {Proceedings of Machine Learning Research}, address = {New York, New York, USA}, month = {20--22 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v48/xuc16.pdf}, url = {https://proceedings.mlr.press/v48/xuc16.html}, abstract = {Learning Granger causality for general point processes is a very challenging task. We propose an effective method learning Granger causality for a special but significant type of point processes — Hawkes processes. Focusing on Hawkes processes, we reveal the relationship between Hawkes process’s impact functions and its Granger causality graph. Specifically, our model represents impact functions using a series of basis functions and recovers the Granger causality graph via group sparsity of the impact functions’ coefficients. We propose an effective learning algorithm combining a maximum likelihood estimator (MLE) with a sparse-group-lasso (SGL) regularizer. Additionally, the pairwise similarity between the dimensions of the process is considered when their clustering structure is available. We analyze our learning method and discuss the selection of the basis functions. Experiments on synthetic data and real-world data show that our method can learn the Granger causality graph and the triggering patterns of Hawkes processes simultaneously.} }
Endnote
%0 Conference Paper %T Learning Granger Causality for Hawkes Processes %A Hongteng Xu %A Mehrdad Farajtabar %A Hongyuan Zha %B Proceedings of The 33rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Maria Florina Balcan %E Kilian Q. Weinberger %F pmlr-v48-xuc16 %I PMLR %P 1717--1726 %U https://proceedings.mlr.press/v48/xuc16.html %V 48 %X Learning Granger causality for general point processes is a very challenging task. We propose an effective method learning Granger causality for a special but significant type of point processes — Hawkes processes. Focusing on Hawkes processes, we reveal the relationship between Hawkes process’s impact functions and its Granger causality graph. Specifically, our model represents impact functions using a series of basis functions and recovers the Granger causality graph via group sparsity of the impact functions’ coefficients. We propose an effective learning algorithm combining a maximum likelihood estimator (MLE) with a sparse-group-lasso (SGL) regularizer. Additionally, the pairwise similarity between the dimensions of the process is considered when their clustering structure is available. We analyze our learning method and discuss the selection of the basis functions. Experiments on synthetic data and real-world data show that our method can learn the Granger causality graph and the triggering patterns of Hawkes processes simultaneously.
RIS
TY - CPAPER TI - Learning Granger Causality for Hawkes Processes AU - Hongteng Xu AU - Mehrdad Farajtabar AU - Hongyuan Zha BT - Proceedings of The 33rd International Conference on Machine Learning DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-xuc16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 1717 EP - 1726 L1 - http://proceedings.mlr.press/v48/xuc16.pdf UR - https://proceedings.mlr.press/v48/xuc16.html AB - Learning Granger causality for general point processes is a very challenging task. We propose an effective method learning Granger causality for a special but significant type of point processes — Hawkes processes. Focusing on Hawkes processes, we reveal the relationship between Hawkes process’s impact functions and its Granger causality graph. Specifically, our model represents impact functions using a series of basis functions and recovers the Granger causality graph via group sparsity of the impact functions’ coefficients. We propose an effective learning algorithm combining a maximum likelihood estimator (MLE) with a sparse-group-lasso (SGL) regularizer. Additionally, the pairwise similarity between the dimensions of the process is considered when their clustering structure is available. We analyze our learning method and discuss the selection of the basis functions. Experiments on synthetic data and real-world data show that our method can learn the Granger causality graph and the triggering patterns of Hawkes processes simultaneously. ER -
APA
Xu, H., Farajtabar, M. & Zha, H.. (2016). Learning Granger Causality for Hawkes Processes. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:1717-1726 Available from https://proceedings.mlr.press/v48/xuc16.html.

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