Self-Attentive Hawkes Process

Qiang Zhang, Aldo Lipani, Omer Kirnap, Emine Yilmaz
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:11183-11193, 2020.

Abstract

Capturing the occurrence dynamics is crucial to predicting which type of events will happen next and when. A common method to do this is through Hawkes processes. To enhance their capacity, recurrent neural networks (RNNs) have been incorporated due to RNNs’ successes in processing sequential data such as languages. Recent evidence suggests that self-attention is more competent than RNNs in dealing with languages. However, we are unaware of the effectiveness of self-attention in the context of Hawkes processes. This study aims to fill the gap by designing a self-attentive Hawkes process (SAHP). SAHP employs self-attention to summarise the influence of history events and compute the probability of the next event. One deficit of the conventional self-attention when applied to event sequences is that its positional encoding only considers the order of a sequence ignoring the time intervals between events. To overcome this deficit, we modify its encoding by translating time intervals into phase shifts of sinusoidal functions. Experiments on goodness-of-fit and prediction tasks show the improved capability of SAHP. Furthermore, SAHP is more interpretable than RNN-based counterparts because the learnt attention weights reveal contributions of one event type to the happening of another type. To the best of our knowledge, this is the first work that studies the effectiveness of self-attention in Hawkes processes.

Cite this Paper


BibTeX
@InProceedings{pmlr-v119-zhang20q, title = {Self-Attentive {H}awkes Process}, author = {Zhang, Qiang and Lipani, Aldo and Kirnap, Omer and Yilmaz, Emine}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {11183--11193}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/zhang20q/zhang20q.pdf}, url = {http://proceedings.mlr.press/v119/zhang20q.html}, abstract = {Capturing the occurrence dynamics is crucial to predicting which type of events will happen next and when. A common method to do this is through Hawkes processes. To enhance their capacity, recurrent neural networks (RNNs) have been incorporated due to RNNs’ successes in processing sequential data such as languages. Recent evidence suggests that self-attention is more competent than RNNs in dealing with languages. However, we are unaware of the effectiveness of self-attention in the context of Hawkes processes. This study aims to fill the gap by designing a self-attentive Hawkes process (SAHP). SAHP employs self-attention to summarise the influence of history events and compute the probability of the next event. One deficit of the conventional self-attention when applied to event sequences is that its positional encoding only considers the order of a sequence ignoring the time intervals between events. To overcome this deficit, we modify its encoding by translating time intervals into phase shifts of sinusoidal functions. Experiments on goodness-of-fit and prediction tasks show the improved capability of SAHP. Furthermore, SAHP is more interpretable than RNN-based counterparts because the learnt attention weights reveal contributions of one event type to the happening of another type. To the best of our knowledge, this is the first work that studies the effectiveness of self-attention in Hawkes processes.} }
Endnote
%0 Conference Paper %T Self-Attentive Hawkes Process %A Qiang Zhang %A Aldo Lipani %A Omer Kirnap %A Emine Yilmaz %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-zhang20q %I PMLR %P 11183--11193 %U http://proceedings.mlr.press/v119/zhang20q.html %V 119 %X Capturing the occurrence dynamics is crucial to predicting which type of events will happen next and when. A common method to do this is through Hawkes processes. To enhance their capacity, recurrent neural networks (RNNs) have been incorporated due to RNNs’ successes in processing sequential data such as languages. Recent evidence suggests that self-attention is more competent than RNNs in dealing with languages. However, we are unaware of the effectiveness of self-attention in the context of Hawkes processes. This study aims to fill the gap by designing a self-attentive Hawkes process (SAHP). SAHP employs self-attention to summarise the influence of history events and compute the probability of the next event. One deficit of the conventional self-attention when applied to event sequences is that its positional encoding only considers the order of a sequence ignoring the time intervals between events. To overcome this deficit, we modify its encoding by translating time intervals into phase shifts of sinusoidal functions. Experiments on goodness-of-fit and prediction tasks show the improved capability of SAHP. Furthermore, SAHP is more interpretable than RNN-based counterparts because the learnt attention weights reveal contributions of one event type to the happening of another type. To the best of our knowledge, this is the first work that studies the effectiveness of self-attention in Hawkes processes.
APA
Zhang, Q., Lipani, A., Kirnap, O. & Yilmaz, E.. (2020). Self-Attentive Hawkes Process. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:11183-11193 Available from http://proceedings.mlr.press/v119/zhang20q.html.

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