Intensity-free Integral-based Learning of Marked Temporal Point Processes

TL;DR

This paper introduces IFIB, a novel intensity-free integral-based framework for modeling the joint distribution of event times and marks in marked temporal point processes, bypassing the need for predefined intensity functions.

Contribution

It proposes a new method that directly models the joint PDF of event marks and times without intensity functions, simplifying the process and improving fidelity.

Findings

IFIB achieves superior results on real-world datasets.

The method simplifies modeling by removing intensity function specification.

Experimental results demonstrate high fidelity in modeling marked temporal point processes.

Abstract

In the marked temporal point processes (MTPP), a core problem is to parameterize the conditional joint PDF (probability distribution function) $p^*(m,t)$ for inter-event time $t$ and mark $m$, conditioned on the history. The majority of existing studies predefine intensity functions. Their utility is challenged by specifying the intensity function's proper form, which is critical to balance expressiveness and processing efficiency. Recently, there are studies moving away from predefining the intensity function -- one models $p^*(t)$ and $p^*(m)$ separately, while the other focuses on temporal point processes (TPPs), which do not consider marks. This study aims to develop high-fidelity $p^*(m,t)$ for discrete events where the event marks are either categorical or numeric in a multi-dimensional continuous space. We propose a solution framework IFIB (\underline{I}ntensity-\underline{f}ree \underline{I}ntegral-\underline{b}ased process) that models conditional joint PDF $p^*(m,t)$ directly without intensity functions. It remarkably simplifies the process to compel the essential mathematical restrictions. We show the desired properties of IFIB and the superior experimental results of IFIB on real-world and synthetic datasets. The code is available at \url{https://github.com/StepinSilence/IFIB}.