Distribution-Free Conformal Joint Prediction Regions for Neural Marked Temporal Point Processes

Aug 5, 2026

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Sequences of labeled events observed at irregular intervals in continuous time arise across many application domains. Temporal point processes provide a modeling framework for inferring future arrival times and event marks, yet uncertainty estimates from probabilistic neural models can be unreliable under misspecification or limited training. The work introduces conformal prediction methods for neural temporal point processes, targeting a distribution-free joint prediction region for time and mark with finite-sample marginal coverage. It handles jointly positive continuous times and categorical marks without distributional assumptions, yielding sharper, dependency-aware regions and studying conditional coverage via experiments.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages51

Reading Time2 h 9 min

AccessFree to download

Introduction

Problem setting and motivation

Temporal point processes and neural models

Conformal prediction for uncertainty quantification

Distribution-free joint prediction regions

Handling continuous time and categorical marks

Methods and evaluation

Univariate conformal regression/classification

Conditional coverage analysis

Experiments on simulated and real data

arXiv :2401 .046 12v2 [ cs .LG] 5 Jun 2024 Distribution-Free Conformal Joint Prediction Regions for Neural Marked Temporal Point Processes Victor Dheur 1*†, Tanguy Bosser 1†, Rafael Izbicki2 , Souhaib Ben Taieb 1 1* Department of Computer Science, University of Mons, Mons, 7000, Belgium. 2* Departamento de Estatistica, Universidade Federal de S˜ao Carlos, S˜ao Carlos, SP 13565-905, Brazil. *Corresponding author(s). E-mail(s): [victor.dheur@umons.ac.be](victor.dheur@umons.ac.be) ; Contributing authors: [tanguy.bosser@umons.ac.be](tanguy.bosser@umons.ac.be) ; [rizbicki@ufscar.br](rizbicki@ufscar.br) ; [souhaib.bentaieb@umons.ac.be](souhaib.bentaieb@umons.ac.be) ; †These authors contributed equally to this work. Abstract 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 overly 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. Keywords: temporal point processes, conformal prediction, bivariate predition region, highest density regions 1 1 Introduction Continuous-time event data often involve sequences of labeled events occurring at irregular intervals, with the number, timing, and mark of these events being random. This type of data is ubiquitous across various fields, ranging from healthcare [1] and neuroscience to finance [2], social media [3], and seismology [4] . In these domains, examples of event sequences include electronic health records, financial transactions, social media activities, and earthquake occurrences. An important task involves predicting not only the timing of future events based on a sequence of observed historical events but also identifying the likely associated label or type of these events, often referred to as ’marks’. Figure 1 shows an example of ten marked event sequences. Temporal Point Processes (TPPs) provide a principled mathematical framework for modeling these event sequences. The main challenge is to learn a TPP model which effectively captures the underlying complex interactions between past event occurrences and future ones. However, classical TPP models, such as the Hawkes process [5], are often constrained by strong assumptions, which can restrict their ability to capture comple

FAQs

What problem does the paper address in neural marked temporal point processes?

It addresses that prediction regions derived from neural TPP probabilistic models can be unreliable when the base model is misspecified or training data are insufficient, leading to poor uncertainty quantification.

What guarantee does the proposed joint prediction region aim to provide?

It aims to construct a distribution-free joint prediction region for an event’s arrival time and mark with a finite-sample marginal coverage guarantee.

How does the method improve over combining separate time and mark prediction regions?

It introduces an approach based on bivariate highest density regions from the joint predictive density, leveraging dependence between time and mark to exclude unlikely combinations while maintaining the target coverage.

Aug 5, 2026

Upload by Ophelia