Learning Network of Multivariate Hawkes Processes: A Time Series Approach

Jalal Etesami, Negar Kiyavash, Kun Zhang, Kushagra Singhal
Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, PMLR R14:662-671, 2016.

Abstract

Learning the influence structure of multiple time series data is of great interest to many disciplines.This paper studies the problem of recovering the causal structure in network of multivariate linear Hawkes processes. In such processes, the occurrence of an event in one process affects the probability of occurrence of new events in some other processes. Thus, a natural notion of causality exists between such processes captured by the support of the excitation matrix.We show that the resulting causal influence network is equivalent to the Directed Information graph (DIG) of the processes, which encodes the causal factorization of the joint distribution of the processes. Furthermore, we present an algorithm for learning the support of excitation matrix of a class of multivariate Hawkes processes with exponential exciting functions (or equivalently the DIG). The performance of the algorithm is evaluated on synthesized multivariate Hawkes networks as well as a stock market and MemeTracker real-world dataset.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR14-etesami16a, title = {Learning Network of Multivariate Hawkes Processes: A Time Series Approach}, author = {Etesami, Jalal and Kiyavash, Negar and Zhang, Kun and Singhal, Kushagra}, booktitle = {Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence}, pages = {662--671}, year = {2016}, editor = {Ihler, Alexander and Janzing, Dominik}, volume = {R14}, series = {Proceedings of Machine Learning Research}, month = {25--29 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r14/main/assets/etesami16a/etesami16a.pdf}, url = {https://proceedings.mlr.press/r14/etesami16a.html}, abstract = {Learning the influence structure of multiple time series data is of great interest to many disciplines.This paper studies the problem of recovering the causal structure in network of multivariate linear Hawkes processes. In such processes, the occurrence of an event in one process affects the probability of occurrence of new events in some other processes. Thus, a natural notion of causality exists between such processes captured by the support of the excitation matrix.We show that the resulting causal influence network is equivalent to the Directed Information graph (DIG) of the processes, which encodes the causal factorization of the joint distribution of the processes. Furthermore, we present an algorithm for learning the support of excitation matrix of a class of multivariate Hawkes processes with exponential exciting functions (or equivalently the DIG). The performance of the algorithm is evaluated on synthesized multivariate Hawkes networks as well as a stock market and MemeTracker real-world dataset.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Learning Network of Multivariate Hawkes Processes: A Time Series Approach %A Jalal Etesami %A Negar Kiyavash %A Kun Zhang %A Kushagra Singhal %B Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2016 %E Alexander Ihler %E Dominik Janzing %F pmlr-vR14-etesami16a %I PMLR %P 662--671 %U https://proceedings.mlr.press/r14/etesami16a.html %V R14 %X Learning the influence structure of multiple time series data is of great interest to many disciplines.This paper studies the problem of recovering the causal structure in network of multivariate linear Hawkes processes. In such processes, the occurrence of an event in one process affects the probability of occurrence of new events in some other processes. Thus, a natural notion of causality exists between such processes captured by the support of the excitation matrix.We show that the resulting causal influence network is equivalent to the Directed Information graph (DIG) of the processes, which encodes the causal factorization of the joint distribution of the processes. Furthermore, we present an algorithm for learning the support of excitation matrix of a class of multivariate Hawkes processes with exponential exciting functions (or equivalently the DIG). The performance of the algorithm is evaluated on synthesized multivariate Hawkes networks as well as a stock market and MemeTracker real-world dataset. %Z Reissued by PMLR on 04 October 2026.
APA
Etesami, J., Kiyavash, N., Zhang, K. & Singhal, K.. (2016). Learning Network of Multivariate Hawkes Processes: A Time Series Approach. Proceedings of the 32nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R14:662-671 Available from https://proceedings.mlr.press/r14/etesami16a.html. Reissued by PMLR on 04 October 2026.

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