Inference and sampling of point processes from diffusion excursions

Ali Hasan, Yu Chen, Yuting Ng, Mohamed Abdelghani, Anderson Schneider, Vahid Tarokh
Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, PMLR 216:839-848, 2023.

Abstract

Point processes often have a natural interpretation with respect to a continuous process. We propose a point process construction that describes arrival time observations in terms of the state of a latent diffusion process. In this framework, we relate the return times of a diffusion in a continuous path space to new arrivals of the point process. This leads to a continuous sample path that is used to describe the underlying mechanism generating the arrival distribution. These models arise in many disciplines, such as financial settings where actions in a market are determined by a hidden continuous price or in neuroscience where a latent stimulus generates spike trains. Based on the developments in Itô’s excursion theory, we propose methods for inferring and sampling from the point process derived from the latent diffusion process. We illustrate the approach with numerical examples using both simulated and real data. The proposed methods and framework provide a basis for interpreting point processes through the lens of diffusions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v216-hasan23a, title = {Inference and sampling of point processes from diffusion excursions}, author = {Hasan, Ali and Chen, Yu and Ng, Yuting and Abdelghani, Mohamed and Schneider, Anderson and Tarokh, Vahid}, booktitle = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence}, pages = {839--848}, year = {2023}, editor = {Evans, Robin J. and Shpitser, Ilya}, volume = {216}, series = {Proceedings of Machine Learning Research}, month = {31 Jul--04 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v216/hasan23a/hasan23a.pdf}, url = {https://proceedings.mlr.press/v216/hasan23a.html}, abstract = {Point processes often have a natural interpretation with respect to a continuous process. We propose a point process construction that describes arrival time observations in terms of the state of a latent diffusion process. In this framework, we relate the return times of a diffusion in a continuous path space to new arrivals of the point process. This leads to a continuous sample path that is used to describe the underlying mechanism generating the arrival distribution. These models arise in many disciplines, such as financial settings where actions in a market are determined by a hidden continuous price or in neuroscience where a latent stimulus generates spike trains. Based on the developments in Itô’s excursion theory, we propose methods for inferring and sampling from the point process derived from the latent diffusion process. We illustrate the approach with numerical examples using both simulated and real data. The proposed methods and framework provide a basis for interpreting point processes through the lens of diffusions.} }
Endnote
%0 Conference Paper %T Inference and sampling of point processes from diffusion excursions %A Ali Hasan %A Yu Chen %A Yuting Ng %A Mohamed Abdelghani %A Anderson Schneider %A Vahid Tarokh %B Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2023 %E Robin J. Evans %E Ilya Shpitser %F pmlr-v216-hasan23a %I PMLR %P 839--848 %U https://proceedings.mlr.press/v216/hasan23a.html %V 216 %X Point processes often have a natural interpretation with respect to a continuous process. We propose a point process construction that describes arrival time observations in terms of the state of a latent diffusion process. In this framework, we relate the return times of a diffusion in a continuous path space to new arrivals of the point process. This leads to a continuous sample path that is used to describe the underlying mechanism generating the arrival distribution. These models arise in many disciplines, such as financial settings where actions in a market are determined by a hidden continuous price or in neuroscience where a latent stimulus generates spike trains. Based on the developments in Itô’s excursion theory, we propose methods for inferring and sampling from the point process derived from the latent diffusion process. We illustrate the approach with numerical examples using both simulated and real data. The proposed methods and framework provide a basis for interpreting point processes through the lens of diffusions.
APA
Hasan, A., Chen, Y., Ng, Y., Abdelghani, M., Schneider, A. & Tarokh, V.. (2023). Inference and sampling of point processes from diffusion excursions. Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 216:839-848 Available from https://proceedings.mlr.press/v216/hasan23a.html.

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