Distribution-Free Conformal Joint Prediction Regions for Neural Marked
  Temporal Point Processes
Victor Dheur Tanguy Bosser Rafael Izbicki Souhaib Ben Taieb
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 the 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
overly conservative approach that combines individual prediction regions for
the event arrival time and mark. Then, we introduce a more effective method
based on bivariate highest density regions derived from the joint predictive
density of event arrival time and mark. By leveraging the dependencies between
these two variables, this method exclude 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 arrival times and marks through conformal regression and
classification techniques. Moreover, we investigate 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.