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Learning multivariate temporal point processes via the time-change theorem

Guilherme Augusto Zagatti · See Kiong Ng · St├ęphane Bressan

MR1 & MR2 - Number 26
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Fri 3 May 8 a.m. PDT — 8:30 a.m. PDT


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.

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