Learning Quantile Functions for Temporal Point Processes with Recurrent Neural Splines

Souhaib Ben Taieb
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:3219-3241, 2022.

Abstract

We can build flexible predictive models for rich continuous-time event data by combining the framework of temporal point processes (TPP) with (recurrent) neural networks. We propose a new neural parametrization for TPPs based on the conditional quantile function. Specifically, we use a flexible monotonic rational-quadratic spline to learn a smooth continuous quantile function. Conditioning on historical events is achieved through a recurrent neural network. This novel parametrization provides a flexible yet tractable TPP model with multiple advantages, such as analytical sampling and closed-form expressions for quantiles and prediction intervals. While neural TPP models are often trained using maximum likelihood estimation, we consider the more robust continuous ranked probability score (CRPS). We additionally derive a closed-form expression for the CRPS of our model. Finally, we demonstrate that the proposed model achieves state-of-the-art performance in standard prediction tasks on both synthetic and real-world event data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-ben-taieb22a, title = { Learning Quantile Functions for Temporal Point Processes with Recurrent Neural Splines }, author = {Ben Taieb, Souhaib}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {3219--3241}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/ben-taieb22a/ben-taieb22a.pdf}, url = {https://proceedings.mlr.press/v151/ben-taieb22a.html}, abstract = { We can build flexible predictive models for rich continuous-time event data by combining the framework of temporal point processes (TPP) with (recurrent) neural networks. We propose a new neural parametrization for TPPs based on the conditional quantile function. Specifically, we use a flexible monotonic rational-quadratic spline to learn a smooth continuous quantile function. Conditioning on historical events is achieved through a recurrent neural network. This novel parametrization provides a flexible yet tractable TPP model with multiple advantages, such as analytical sampling and closed-form expressions for quantiles and prediction intervals. While neural TPP models are often trained using maximum likelihood estimation, we consider the more robust continuous ranked probability score (CRPS). We additionally derive a closed-form expression for the CRPS of our model. Finally, we demonstrate that the proposed model achieves state-of-the-art performance in standard prediction tasks on both synthetic and real-world event data. } }
Endnote
%0 Conference Paper %T Learning Quantile Functions for Temporal Point Processes with Recurrent Neural Splines %A Souhaib Ben Taieb %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-ben-taieb22a %I PMLR %P 3219--3241 %U https://proceedings.mlr.press/v151/ben-taieb22a.html %V 151 %X We can build flexible predictive models for rich continuous-time event data by combining the framework of temporal point processes (TPP) with (recurrent) neural networks. We propose a new neural parametrization for TPPs based on the conditional quantile function. Specifically, we use a flexible monotonic rational-quadratic spline to learn a smooth continuous quantile function. Conditioning on historical events is achieved through a recurrent neural network. This novel parametrization provides a flexible yet tractable TPP model with multiple advantages, such as analytical sampling and closed-form expressions for quantiles and prediction intervals. While neural TPP models are often trained using maximum likelihood estimation, we consider the more robust continuous ranked probability score (CRPS). We additionally derive a closed-form expression for the CRPS of our model. Finally, we demonstrate that the proposed model achieves state-of-the-art performance in standard prediction tasks on both synthetic and real-world event data.
APA
Ben Taieb, S.. (2022). Learning Quantile Functions for Temporal Point Processes with Recurrent Neural Splines . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:3219-3241 Available from https://proceedings.mlr.press/v151/ben-taieb22a.html.

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