Learning multivariate temporal point processes via the time-change theorem
Guilherme Augusto Zagatti, See Kiong Ng, Stéphane Bressan
Abstract
Marked temporal point processes (TPPs) are a class of stochastic processes that describe the occurrence of a countable number of marked events over continuous time. In machine learning, the most common representation of marked TPPs is the univariate TPP coupled with a conditional mark distribution. Alternatively, we can represent marked TPPs as a multivariate temporal point process in which we model each sequence of marks interdependently. We introduce a learning framework for multivariate TPPs leveraging recent progress on learning univariate TPPs via time-change theorems to propose a deep-learning, invertible model for the conditional intensity. We rely neither on Monte Carlo approximation for the compensator nor on thinning for sampling. Therefore, we have a generative model that can efficiently sample the next event given a history of past events. Our models show strong alignment between the percentiles of the distribution expected from theory and the empirical ones.
BibTeX
@InProceedings{pmlr-v238-augusto-zagatti24a,
title = {Learning multivariate temporal point processes via the time-change theorem},
author = {Augusto Zagatti, Guilherme and Kiong Ng, See and Bressan, St\'{e}phane},
booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics},
pages = {3241--3249},
year = {2024},
editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen},
volume = {238},
series = {Proceedings of Machine Learning Research},
month = {02--04 May},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v238/augusto-zagatti24a/augusto-zagatti24a.pdf},
url = {https://proceedings.mlr.press/v238/augusto-zagatti24a.html},
abstract = {Marked temporal point processes (TPPs) are a class of stochastic processes that describe the occurrence of a countable number of marked events over continuous time. In machine learning, the most common representation of marked TPPs is the univariate TPP coupled with a conditional mark distribution. Alternatively, we can represent marked TPPs as a multivariate temporal point process in which we model each sequence of marks interdependently. We introduce a learning framework for multivariate TPPs leveraging recent progress on learning univariate TPPs via time-change theorems to propose a deep-learning, invertible model for the conditional intensity. We rely neither on Monte Carlo approximation for the compensator nor on thinning for sampling. Therefore, we have a generative model that can efficiently sample the next event given a history of past events. Our models show strong alignment between the percentiles of the distribution expected from theory and the empirical ones.}
}