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Addressing Mark Imbalance in Integration-free Neural Marked Temporal Point Processes

Sishun Liu, Ke Deng, Yongli Ren, Yan Wang, Xiuzhen Zhang

TL;DR

This paper addresses the challenge of mark imbalance in neural Marked Temporal Point Processes (MTPP) by proposing thresholding on the mark probability normalized by the mark prior, to improve rare-mark prediction. It adopts a mark-first, time-second strategy and introduces a novel integration-unifying model (*model) that enables direct estimation of $p^*(m)$ and the CDF of $p^*(t|m)$ via $\Gamma^*(m,t)$, avoiding costly numerical integration. The method demonstrates superior performance over baselines on real-world datasets for both next-event marks and times, and provides extensive experiments including synthetic data fidelity and ablations. The work offers a practical, bias-aware approach to imbalanced MTPPPs with a clear path toward real-world deployment and further bias-aware developments.

Abstract

Marked Temporal Point Process (MTPP) has been well studied to model the event distribution in marked event streams, which can be used to predict the mark and arrival time of the next event. However, existing studies overlook that the distribution of event marks is highly imbalanced in many real-world applications, with some marks being frequent but others rare. The imbalance poses a significant challenge to the performance of the next event prediction, especially for events of rare marks. To address this issue, we propose a thresholding method, which learns thresholds to tune the mark probability normalized by the mark's prior probability to optimize mark prediction, rather than predicting the mark directly based on the mark probability as in existing studies. In conjunction with this method, we predict the mark first and then the time. In particular, we develop a novel neural MTPP model to support effective time sampling and estimation of mark probability without computationally expensive numerical improper integration. Extensive experiments on real-world datasets demonstrate the superior performance of our solution against various baselines for the next event mark and time prediction. The code is available at https://github.com/undes1red/IFNMTPP.

Addressing Mark Imbalance in Integration-free Neural Marked Temporal Point Processes

TL;DR

This paper addresses the challenge of mark imbalance in neural Marked Temporal Point Processes (MTPP) by proposing thresholding on the mark probability normalized by the mark prior, to improve rare-mark prediction. It adopts a mark-first, time-second strategy and introduces a novel integration-unifying model (*model) that enables direct estimation of and the CDF of via , avoiding costly numerical integration. The method demonstrates superior performance over baselines on real-world datasets for both next-event marks and times, and provides extensive experiments including synthetic data fidelity and ablations. The work offers a practical, bias-aware approach to imbalanced MTPPPs with a clear path toward real-world deployment and further bias-aware developments.

Abstract

Marked Temporal Point Process (MTPP) has been well studied to model the event distribution in marked event streams, which can be used to predict the mark and arrival time of the next event. However, existing studies overlook that the distribution of event marks is highly imbalanced in many real-world applications, with some marks being frequent but others rare. The imbalance poses a significant challenge to the performance of the next event prediction, especially for events of rare marks. To address this issue, we propose a thresholding method, which learns thresholds to tune the mark probability normalized by the mark's prior probability to optimize mark prediction, rather than predicting the mark directly based on the mark probability as in existing studies. In conjunction with this method, we predict the mark first and then the time. In particular, we develop a novel neural MTPP model to support effective time sampling and estimation of mark probability without computationally expensive numerical improper integration. Extensive experiments on real-world datasets demonstrate the superior performance of our solution against various baselines for the next event mark and time prediction. The code is available at https://github.com/undes1red/IFNMTPP.
Paper Structure (41 sections, 1 theorem, 34 equations, 3 figures, 17 tables)

This paper contains 41 sections, 1 theorem, 34 equations, 3 figures, 17 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Marked Temporal Point Process
  4. Mark Imbalance
  5. Methodology
  6. Next Event Mark Prediction with Thresholding
  7. Next Event Time Prediction
  8. Unifying Integral Functions
  9. *model
  10. Experiments
  11. Experiment results
  12. Related Work
  13. Conclusion and Limitation
  14. The Conditional Joint PDF
  15. Proof of the Proposition 3.1
  16. ...and 26 more sections

Key Result

Proposition 3.1

The output of *model is $\Gamma^*(m, t)$ when its gradient is $-p^*(m, t)$.

Figures (3)

  • Figure 1: Mark prediction performance measured by macro-F1 using SAHP zhang_self-attentive_2020 for rare and frequent marks on three real-world datasets.
  • Figure 2: Architecture of *model where the history encoder is an LSTM.
  • Figure 3: The frequency distribution of marks in real-world datasets.

Theorems & Definitions (2)

  • Proposition 3.1
  • proof