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

arXiv: https://arxiv.org/abs/2401.04612 · HTML: https://mlsanity.com/paper/2401.04612/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 72 references that are in the map.
- First posted on arXiv 9 Jan 2024.

## Builds on (most cited first, 30 of 42)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Predicting Dynamic Embedding Trajectory in Temporal Interaction Networks](https://mlsanity.com/paper/1908.01207/) (2019)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Intensity-Free Learning of Temporal Point Processes](https://mlsanity.com/paper/1909.12127/) (2019)
- [Fully Neural Network based Model for General Temporal Point Processes](https://mlsanity.com/paper/1905.09690/) (2019)
- [Neural Temporal Point Processes: A Review](https://mlsanity.com/paper/2104.03528/) (2021)
- [Transformer Embeddings of Irregularly Spaced Events and Their Participants](https://mlsanity.com/paper/2201.00044/) (2021)
- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [Conformal Prediction using Conditional Histograms](https://mlsanity.com/paper/2105.08747/) (2021)
- [A comparison of some conformal quantile regression methods](https://mlsanity.com/paper/1909.05433/) (2019)
- [CD-split and HPD-split: efficient conformal regions in high dimensions](https://mlsanity.com/paper/2007.12778/) (2020)
- [Conformal prediction for time series](https://mlsanity.com/paper/2010.09107/) (2020)
- [Conformalized Survival Analysis](https://mlsanity.com/paper/2103.09763/) (2021)
- [Calibrated Multiple-Output Quantile Regression with Representation Learning](https://mlsanity.com/paper/2110.00816/) (2021)
- [Wasserstein Learning of Deep Generative Point Process Models](https://mlsanity.com/paper/1705.08051/) (2017)
- [Lecture Notes: Temporal Point Processes and the Conditional Intensity Function](https://mlsanity.com/paper/1806.00221/) (2018)
- [Learning Temporal Point Processes via Reinforcement Learning](https://mlsanity.com/paper/1811.05016/) (2018)
- [Neural Temporal Point Processes For Modelling Electronic Health Records](https://mlsanity.com/paper/2007.13794/) (2020)
- [COEVOLVE: A Joint Point Process Model for Information Diffusion and Network Co-evolution](https://mlsanity.com/paper/1507.02293/) (2015)
- [Distribution-Free Prediction Sets for Two-Layer Hierarchical Models](https://mlsanity.com/paper/1809.07441/) (2018)

## Built on by (most cited first, 7 of 7)

- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Rectifying Conformity Scores for Better Conditional Coverage](https://mlsanity.com/paper/2502.16336/) (2025)
- [Epistemic Uncertainty in Conformal Scores: A Unified Approach](https://mlsanity.com/paper/2502.06995/) (2025)
- [Conformal Calibration of Statistical Confidence Sets](https://mlsanity.com/paper/2411.19368/) (2024)
- [Reliable uncertainty quantification for 2D/3D anatomical landmark localization using multi-output conformal prediction](https://mlsanity.com/paper/2503.14106/) (2025)
- [Hierarchical Probabilistic Conformal Prediction for Distributed Energy Resources Adoption](https://mlsanity.com/paper/2411.12193/) (2024)
- [LoBoost: Fast Model-Native Local Conformal Prediction for Gradient-Boosted Trees](https://mlsanity.com/paper/2602.22432/) (2026)

## Abstract (arXiv)

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.