  Sequences of labeled events observed at irregular intervals in continuous
time are ubiquitous across various fields. Temporal Point Processes (TPPs)
provide a mathematical framework for modeling these sequences, enabling
inferences such as predicting the arrival time of future events and their
associated label, called mark. However, due to model misspecification or lack
of training data, these probabilistic models may provide a poor approximation
of the true, unknown underlying process, with prediction regions extracted from
them being unreliable estimates of the underlying uncertainty. This paper
develops more reliable methods for uncertainty quantification in neural TPP
models via the framework of conformal prediction. A primary objective is to
generate a distribution-free joint prediction region for an event's arrival
time and mark, with a finite-sample marginal coverage guarantee. A key
challenge is to handle both a strictly positive, continuous response and a
categorical response, without distributional assumptions. We first consider a
simple but conservative approach that combines individual prediction regions
for the event's arrival time and mark. Then, we introduce a more effective
method based on bivariate highest density regions derived from the joint
predictive density of arrival times and marks. By leveraging the dependencies
between these two variables, this method excludes unlikely combinations of the
two, resulting in sharper prediction regions while still attaining the
pre-specified coverage level. We also explore the generation of individual
univariate prediction regions for events' arrival times and marks through
conformal regression and classification techniques. Moreover, we evaluate the
stronger notion of conditional coverage. Finally, through extensive
experimentation on both simulated and real-world datasets, we assess the
validity and efficiency of these methods.
