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# Learning multivariate temporal point processes via the time-change theorem

*Proceedings of The 27th International Conference on Artificial Intelligence and Statistics*, PMLR 238:3241-3249, 2024.

#### 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.