Learning Social Infectivity in Sparse Low-rank Networks Using Multi-dimensional Hawkes Processes

Ke Zhou, Hongyuan Zha, Le Song
Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, PMLR 31:641-649, 2013.

Abstract

How will the behaviors of individuals in a social network be influenced by their neighbors, the authorities and the communities? Such knowledge is often hidden from us and we only observe its manifestation in the form of recurrent and time-stamped events occurring at the individuals involved. It is an important yet challenging problem to infer the network of social inference based on the temporal patterns of these historical events. We propose a convex optimization approach to discover the hidden network of social influence by modeling the recurrent events at different individuals as multi-dimensional Hawkes processes. Furthermore, our estimation procedure, using nuclear and \ell_1 norm regularization simultaneously on the parameters, is able to take into account the prior knowledge of the presence of neighbor interaction, authority influence, and community coordination. To efficiently solve the problem, we also design an algorithm ADM4 which combines techniques of alternating direction method of multipliers and majorization minimization. We experimented with both synthetic and real world data sets, and showed that the proposed method can discover the hidden network more accurately and produce a better predictive model.

Cite this Paper

BibTeX
@InProceedings{pmlr-v31-zhou13a, title = {Learning Social Infectivity in Sparse Low-rank Networks Using Multi-dimensional Hawkes Processes}, author = {Zhou, Ke and Zha, Hongyuan and Song, Le}, booktitle = {Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics}, pages = {641--649}, year = {2013}, editor = {Carvalho, Carlos M. and Ravikumar, Pradeep}, volume = {31}, series = {Proceedings of Machine Learning Research}, address = {Scottsdale, Arizona, USA}, month = {29 Apr--01 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v31/zhou13a.pdf}, url = {https://proceedings.mlr.press/v31/zhou13a.html}, abstract = {How will the behaviors of individuals in a social network be influenced by their neighbors, the authorities and the communities? Such knowledge is often hidden from us and we only observe its manifestation in the form of recurrent and time-stamped events occurring at the individuals involved. It is an important yet challenging problem to infer the network of social inference based on the temporal patterns of these historical events. We propose a convex optimization approach to discover the hidden network of social influence by modeling the recurrent events at different individuals as multi-dimensional Hawkes processes. Furthermore, our estimation procedure, using nuclear and \ell_1 norm regularization simultaneously on the parameters, is able to take into account the prior knowledge of the presence of neighbor interaction, authority influence, and community coordination. To efficiently solve the problem, we also design an algorithm ADM4 which combines techniques of alternating direction method of multipliers and majorization minimization. We experimented with both synthetic and real world data sets, and showed that the proposed method can discover the hidden network more accurately and produce a better predictive model.} }
Endnote
%0 Conference Paper %T Learning Social Infectivity in Sparse Low-rank Networks Using Multi-dimensional Hawkes Processes %A Ke Zhou %A Hongyuan Zha %A Le Song %B Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2013 %E Carlos M. Carvalho %E Pradeep Ravikumar %F pmlr-v31-zhou13a %I PMLR %P 641--649 %U https://proceedings.mlr.press/v31/zhou13a.html %V 31 %X How will the behaviors of individuals in a social network be influenced by their neighbors, the authorities and the communities? Such knowledge is often hidden from us and we only observe its manifestation in the form of recurrent and time-stamped events occurring at the individuals involved. It is an important yet challenging problem to infer the network of social inference based on the temporal patterns of these historical events. We propose a convex optimization approach to discover the hidden network of social influence by modeling the recurrent events at different individuals as multi-dimensional Hawkes processes. Furthermore, our estimation procedure, using nuclear and \ell_1 norm regularization simultaneously on the parameters, is able to take into account the prior knowledge of the presence of neighbor interaction, authority influence, and community coordination. To efficiently solve the problem, we also design an algorithm ADM4 which combines techniques of alternating direction method of multipliers and majorization minimization. We experimented with both synthetic and real world data sets, and showed that the proposed method can discover the hidden network more accurately and produce a better predictive model.
RIS
TY - CPAPER TI - Learning Social Infectivity in Sparse Low-rank Networks Using Multi-dimensional Hawkes Processes AU - Ke Zhou AU - Hongyuan Zha AU - Le Song BT - Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics DA - 2013/04/29 ED - Carlos M. Carvalho ED - Pradeep Ravikumar ID - pmlr-v31-zhou13a PB - PMLR DP - Proceedings of Machine Learning Research VL - 31 SP - 641 EP - 649 L1 - http://proceedings.mlr.press/v31/zhou13a.pdf UR - https://proceedings.mlr.press/v31/zhou13a.html AB - How will the behaviors of individuals in a social network be influenced by their neighbors, the authorities and the communities? Such knowledge is often hidden from us and we only observe its manifestation in the form of recurrent and time-stamped events occurring at the individuals involved. It is an important yet challenging problem to infer the network of social inference based on the temporal patterns of these historical events. We propose a convex optimization approach to discover the hidden network of social influence by modeling the recurrent events at different individuals as multi-dimensional Hawkes processes. Furthermore, our estimation procedure, using nuclear and \ell_1 norm regularization simultaneously on the parameters, is able to take into account the prior knowledge of the presence of neighbor interaction, authority influence, and community coordination. To efficiently solve the problem, we also design an algorithm ADM4 which combines techniques of alternating direction method of multipliers and majorization minimization. We experimented with both synthetic and real world data sets, and showed that the proposed method can discover the hidden network more accurately and produce a better predictive model. ER -
APA
Zhou, K., Zha, H. & Song, L.. (2013). Learning Social Infectivity in Sparse Low-rank Networks Using Multi-dimensional Hawkes Processes. Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 31:641-649 Available from https://proceedings.mlr.press/v31/zhou13a.html.

Related Material