Hawkes Process with Flexible Triggering Kernels

Yamac Isik, Paidamoyo Chapfuwa, Connor Davis, Ricardo Henao
Proceedings of the 8th Machine Learning for Healthcare Conference, PMLR 219:308-320, 2023.

Abstract

Recently proposed encoder-decoder structures for modeling Hawkes processes use transformer-inspired architectures, which encode the history of events via embeddings and self-attention mechanisms. These models deliver better prediction and goodness-of-fit than their RNN-based counterparts. However, they often require high computational and memory complexity and fail to adequately capture the triggering function of the underlying process. So motivated, we introduce an efficient and general encoding of the historical event sequence by replacing the complex (multilayered) attention structures with triggering kernels of the observed data. Noting the similarity between the triggering kernels of a point process and the attention scores, we use a triggering kernel to replace the weights used to build history representations. Our estimator for the triggering function is equipped with a sigmoid gating mechanism that captures local-in-time triggering effects that are otherwise challenging with standard decaying-over-time kernels. Further, taking both event type representations and temporal embeddings as inputs, the model learns the underlying triggering type-time kernel parameters given pairs of event types. We present experiments on synthetic and real data sets widely used by competing models, and further include a COVID-19 dataset to illustrate the use of longitudinal covariates. Our results show the proposed model outperforms existing approaches, is more efficient in terms of computational complexity, and yields interpretable results via direct application of the newly introduced kernel.

Cite this Paper

BibTeX
@InProceedings{pmlr-v219-isik23a, title = {Hawkes Process with Flexible Triggering Kernels}, author = {Isik, Yamac and Chapfuwa, Paidamoyo and Davis, Connor and Henao, Ricardo}, booktitle = {Proceedings of the 8th Machine Learning for Healthcare Conference}, pages = {308--320}, year = {2023}, editor = {Deshpande, Kaivalya and Fiterau, Madalina and Joshi, Shalmali and Lipton, Zachary and Ranganath, Rajesh and Urteaga, Iñigo and Yeung, Serene}, volume = {219}, series = {Proceedings of Machine Learning Research}, month = {11--12 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v219/isik23a/isik23a.pdf}, url = {https://proceedings.mlr.press/v219/isik23a.html}, abstract = {Recently proposed encoder-decoder structures for modeling Hawkes processes use transformer-inspired architectures, which encode the history of events via embeddings and self-attention mechanisms. These models deliver better prediction and goodness-of-fit than their RNN-based counterparts. However, they often require high computational and memory complexity and fail to adequately capture the triggering function of the underlying process. So motivated, we introduce an efficient and general encoding of the historical event sequence by replacing the complex (multilayered) attention structures with triggering kernels of the observed data. Noting the similarity between the triggering kernels of a point process and the attention scores, we use a triggering kernel to replace the weights used to build history representations. Our estimator for the triggering function is equipped with a sigmoid gating mechanism that captures local-in-time triggering effects that are otherwise challenging with standard decaying-over-time kernels. Further, taking both event type representations and temporal embeddings as inputs, the model learns the underlying triggering type-time kernel parameters given pairs of event types. We present experiments on synthetic and real data sets widely used by competing models, and further include a COVID-19 dataset to illustrate the use of longitudinal covariates. Our results show the proposed model outperforms existing approaches, is more efficient in terms of computational complexity, and yields interpretable results via direct application of the newly introduced kernel.} }
Endnote
%0 Conference Paper %T Hawkes Process with Flexible Triggering Kernels %A Yamac Isik %A Paidamoyo Chapfuwa %A Connor Davis %A Ricardo Henao %B Proceedings of the 8th Machine Learning for Healthcare Conference %C Proceedings of Machine Learning Research %D 2023 %E Kaivalya Deshpande %E Madalina Fiterau %E Shalmali Joshi %E Zachary Lipton %E Rajesh Ranganath %E Iñigo Urteaga %E Serene Yeung %F pmlr-v219-isik23a %I PMLR %P 308--320 %U https://proceedings.mlr.press/v219/isik23a.html %V 219 %X Recently proposed encoder-decoder structures for modeling Hawkes processes use transformer-inspired architectures, which encode the history of events via embeddings and self-attention mechanisms. These models deliver better prediction and goodness-of-fit than their RNN-based counterparts. However, they often require high computational and memory complexity and fail to adequately capture the triggering function of the underlying process. So motivated, we introduce an efficient and general encoding of the historical event sequence by replacing the complex (multilayered) attention structures with triggering kernels of the observed data. Noting the similarity between the triggering kernels of a point process and the attention scores, we use a triggering kernel to replace the weights used to build history representations. Our estimator for the triggering function is equipped with a sigmoid gating mechanism that captures local-in-time triggering effects that are otherwise challenging with standard decaying-over-time kernels. Further, taking both event type representations and temporal embeddings as inputs, the model learns the underlying triggering type-time kernel parameters given pairs of event types. We present experiments on synthetic and real data sets widely used by competing models, and further include a COVID-19 dataset to illustrate the use of longitudinal covariates. Our results show the proposed model outperforms existing approaches, is more efficient in terms of computational complexity, and yields interpretable results via direct application of the newly introduced kernel.
APA
Isik, Y., Chapfuwa, P., Davis, C. & Henao, R.. (2023). Hawkes Process with Flexible Triggering Kernels. Proceedings of the 8th Machine Learning for Healthcare Conference, in Proceedings of Machine Learning Research 219:308-320 Available from https://proceedings.mlr.press/v219/isik23a.html.

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