Temporal Logic Point Processes

Shuang Li, Lu Wang, Ruizhi Zhang, Xiaofu Chang, Xuqin Liu, Yao Xie, Yuan Qi, Le Song
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:5990-6000, 2020.

Abstract

We propose a modeling framework for event data and aim to answer questions such as \emph{when} and \emph{why} the next event would happen. Our proposed model excels in small data regime with the ability to incorporate domain knowledge in terms of logic rules. We model the dynamics of the event starts and ends via intensity function with the structures informed by a set of first-order temporal logic rules. Using the softened representation of temporal relations, and a weighted combination of logic rules, our probabilistic model can deal with uncertainty in events. Furthermore, many well-known point processes (e.g., Hawkes process, self-correcting point process) can be interpreted as special cases of our model given simple temporal logic rules. Our model, therefore, riches the family of point processes. We derive a maximum likelihood estimation procedure for our model and show that it can lead to accurate predictions when data are sparse and domain knowledge is critical.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-li20p, title = {Temporal Logic Point Processes}, author = {Li, Shuang and Wang, Lu and Zhang, Ruizhi and Chang, Xiaofu and Liu, Xuqin and Xie, Yao and Qi, Yuan and Song, Le}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {5990--6000}, 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/li20p/li20p.pdf}, url = {https://proceedings.mlr.press/v119/li20p.html}, abstract = {We propose a modeling framework for event data and aim to answer questions such as \emph{when} and \emph{why} the next event would happen. Our proposed model excels in small data regime with the ability to incorporate domain knowledge in terms of logic rules. We model the dynamics of the event starts and ends via intensity function with the structures informed by a set of first-order temporal logic rules. Using the softened representation of temporal relations, and a weighted combination of logic rules, our probabilistic model can deal with uncertainty in events. Furthermore, many well-known point processes (e.g., Hawkes process, self-correcting point process) can be interpreted as special cases of our model given simple temporal logic rules. Our model, therefore, riches the family of point processes. We derive a maximum likelihood estimation procedure for our model and show that it can lead to accurate predictions when data are sparse and domain knowledge is critical.} }
Endnote
%0 Conference Paper %T Temporal Logic Point Processes %A Shuang Li %A Lu Wang %A Ruizhi Zhang %A Xiaofu Chang %A Xuqin Liu %A Yao Xie %A Yuan Qi %A Le Song %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-li20p %I PMLR %P 5990--6000 %U https://proceedings.mlr.press/v119/li20p.html %V 119 %X We propose a modeling framework for event data and aim to answer questions such as \emph{when} and \emph{why} the next event would happen. Our proposed model excels in small data regime with the ability to incorporate domain knowledge in terms of logic rules. We model the dynamics of the event starts and ends via intensity function with the structures informed by a set of first-order temporal logic rules. Using the softened representation of temporal relations, and a weighted combination of logic rules, our probabilistic model can deal with uncertainty in events. Furthermore, many well-known point processes (e.g., Hawkes process, self-correcting point process) can be interpreted as special cases of our model given simple temporal logic rules. Our model, therefore, riches the family of point processes. We derive a maximum likelihood estimation procedure for our model and show that it can lead to accurate predictions when data are sparse and domain knowledge is critical.
APA
Li, S., Wang, L., Zhang, R., Chang, X., Liu, X., Xie, Y., Qi, Y. & Song, L.. (2020). Temporal Logic Point Processes. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:5990-6000 Available from https://proceedings.mlr.press/v119/li20p.html.

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