Learning Triggering Kernels for Multi-dimensional Hawkes Processes

Ke Zhou; Hongyuan Zha; Le Song

Learning Triggering Kernels for Multi-dimensional Hawkes Processes

Ke Zhou, Hongyuan Zha, Le Song ;

Proceedings of the 30th International Conference on Machine Learning, PMLR 28(3):1301-1309, 2013.

Abstract

How does the activity of one person affect that of another person? Does the strength of influence remain periodic or decay exponentially over time? In this paper, we study these critical questions in social network analysis quantitatively under the framework of multi-dimensional Hawkes processes. In particular, we focus on the nonparametric learning of the triggering kernels, and propose an algorithm \sf MMEL that combines the idea of decoupling the parameters through constructing a tight upper-bound of the objective function and application of Euler-Lagrange equations for optimization in infinite dimensional functional space. We show that the proposed method performs significantly better than alternatives in experiments on both synthetic and real world datasets.

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@InProceedings{pmlr-v28-zhou13, title = {Learning Triggering Kernels for Multi-dimensional Hawkes Processes}, author = {Ke Zhou and Hongyuan Zha and Le Song}, booktitle = {Proceedings of the 30th International Conference on Machine Learning}, pages = {1301--1309}, year = {2013}, editor = {Sanjoy Dasgupta and David McAllester}, volume = {28}, number = {3}, series = {Proceedings of Machine Learning Research}, address = {Atlanta, Georgia, USA}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v28/zhou13.pdf}, url = {http://proceedings.mlr.press/v28/zhou13.html}, abstract = {How does the activity of one person affect that of another person? Does the strength of influence remain periodic or decay exponentially over time? In this paper, we study these critical questions in social network analysis quantitatively under the framework of multi-dimensional Hawkes processes. In particular, we focus on the nonparametric learning of the triggering kernels, and propose an algorithm \sf MMEL that combines the idea of decoupling the parameters through constructing a tight upper-bound of the objective function and application of Euler-Lagrange equations for optimization in infinite dimensional functional space. We show that the proposed method performs significantly better than alternatives in experiments on both synthetic and real world datasets. } }

%0 Conference Paper %T Learning Triggering Kernels for Multi-dimensional Hawkes Processes %A Ke Zhou %A Hongyuan Zha %A Le Song %B Proceedings of the 30th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2013 %E Sanjoy Dasgupta %E David McAllester %F pmlr-v28-zhou13 %I PMLR %J Proceedings of Machine Learning Research %P 1301--1309 %U http://proceedings.mlr.press %V 28 %N 3 %W PMLR %X How does the activity of one person affect that of another person? Does the strength of influence remain periodic or decay exponentially over time? In this paper, we study these critical questions in social network analysis quantitatively under the framework of multi-dimensional Hawkes processes. In particular, we focus on the nonparametric learning of the triggering kernels, and propose an algorithm \sf MMEL that combines the idea of decoupling the parameters through constructing a tight upper-bound of the objective function and application of Euler-Lagrange equations for optimization in infinite dimensional functional space. We show that the proposed method performs significantly better than alternatives in experiments on both synthetic and real world datasets.

TY - CPAPER TI - Learning Triggering Kernels for Multi-dimensional Hawkes Processes AU - Ke Zhou AU - Hongyuan Zha AU - Le Song BT - Proceedings of the 30th International Conference on Machine Learning PY - 2013/02/13 DA - 2013/02/13 ED - Sanjoy Dasgupta ED - David McAllester ID - pmlr-v28-zhou13 PB - PMLR SP - 1301 DP - PMLR EP - 1309 L1 - http://proceedings.mlr.press/v28/zhou13.pdf UR - http://proceedings.mlr.press/v28/zhou13.html AB - How does the activity of one person affect that of another person? Does the strength of influence remain periodic or decay exponentially over time? In this paper, we study these critical questions in social network analysis quantitatively under the framework of multi-dimensional Hawkes processes. In particular, we focus on the nonparametric learning of the triggering kernels, and propose an algorithm \sf MMEL that combines the idea of decoupling the parameters through constructing a tight upper-bound of the objective function and application of Euler-Lagrange equations for optimization in infinite dimensional functional space. We show that the proposed method performs significantly better than alternatives in experiments on both synthetic and real world datasets. ER -

Zhou, K., Zha, H. & Song, L.. (2013). Learning Triggering Kernels for Multi-dimensional Hawkes Processes. Proceedings of the 30th International Conference on Machine Learning, in PMLR 28(3):1301-1309