Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Marked Temporal Bayesian Flow Point Processes

Hui Chen, Xuhui Fan, Hengyu Liu, Longbing Cao

TL;DR

Unlike existing generative MTPP models, BMTPP flexibly models marked temporal joint distributions using a parameter-based approach and effectively captures and explicitly reveals the interdependence between timestamps and event types.

Abstract

Marked event data captures events by recording their continuous-valued occurrence timestamps along with their corresponding discrete-valued types. They have appeared in various real-world scenarios such as social media, financial transactions, and healthcare records, and have been effectively modeled through Marked Temporal Point Process (MTPP) models. Recently, developing generative models for these MTPP models have seen rapid development due to their powerful generative capability and less restrictive functional forms. However, existing generative MTPP models are usually challenged in jointly modeling events' timestamps and types since: (1) mainstream methods design the generative mechanisms for timestamps only and do not include event types; (2) the complex interdependence between the timestamps and event types are overlooked. In this paper, we propose a novel generative MTPP model called BMTPP. Unlike existing generative MTPP models, BMTPP flexibly models marked temporal joint distributions using a parameter-based approach. Additionally, by adding joint noise to the marked temporal data space, BMTPP effectively captures and explicitly reveals the interdependence between timestamps and event types. Extensive experiments validate the superiority of our approach over other state-of-the-art models and its ability to effectively capture marked-temporal interdependence.

Marked Temporal Bayesian Flow Point Processes

TL;DR

Unlike existing generative MTPP models, BMTPP flexibly models marked temporal joint distributions using a parameter-based approach and effectively captures and explicitly reveals the interdependence between timestamps and event types.

Abstract

Marked event data captures events by recording their continuous-valued occurrence timestamps along with their corresponding discrete-valued types. They have appeared in various real-world scenarios such as social media, financial transactions, and healthcare records, and have been effectively modeled through Marked Temporal Point Process (MTPP) models. Recently, developing generative models for these MTPP models have seen rapid development due to their powerful generative capability and less restrictive functional forms. However, existing generative MTPP models are usually challenged in jointly modeling events' timestamps and types since: (1) mainstream methods design the generative mechanisms for timestamps only and do not include event types; (2) the complex interdependence between the timestamps and event types are overlooked. In this paper, we propose a novel generative MTPP model called BMTPP. Unlike existing generative MTPP models, BMTPP flexibly models marked temporal joint distributions using a parameter-based approach. Additionally, by adding joint noise to the marked temporal data space, BMTPP effectively captures and explicitly reveals the interdependence between timestamps and event types. Extensive experiments validate the superiority of our approach over other state-of-the-art models and its ability to effectively capture marked-temporal interdependence.

Paper Structure

This paper contains 21 sections, 1 theorem, 27 equations, 4 figures, 4 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Marked Temporal Point Processes
  4. Bayesian Flow Networks
  5. Marked Temporal Bayesian Flow Point Processes
  6. Formulation of Time Intervals $\tau$
  7. Formulation of Marks $m$
  8. Joint Noise Strategy
  9. Algorithm
  10. Experiments
  11. Experimental Setup
  12. Performance Comparison
  13. Analysis of Vector $\mathbf{c}$
  14. Ablation Study
  15. Hyperparameter Sensitivity Analysis
  16. ...and 6 more sections

Key Result

Proposition 1

To make sure the matrix ${\boldsymbol{\mathbf{\Sigma}}}_{\tau, m}$ is positive definite, ${\boldsymbol{\mathbf{c}}}$ is restricted as ${\boldsymbol{\mathbf{c}}}^{\top}{\boldsymbol{\mathbf{c}}}<M$.

Figures (4)

  • Figure 1: The framework of BMTPP. We aim to learn the marked temporal joint distribution conditioned on the historical embedding $\mathbf{h}_{i-1}$ generated by the historical encoder.
  • Figure 2: The number of elements from vector $\mathbf{c}$ across different value ranges on four real-world datasets.
  • Figure 3: Ablation study. W/ JN and W/O JN represent the model with and without the joint noise strategy, respectively.
  • Figure 4: Performance comparison on four real-world datasets with varying sampling steps.

Theorems & Definitions (2)

  • Proposition 1
  • proof