Conditional Generative Modeling for High-dimensional Marked Temporal Point Processes

TL;DR

The paper tackles the challenge of modeling temporal point processes with high-dimensional marks by replacing explicit conditional intensity modeling with a conditional event generator (CEG) that samples future events from history. It introduces a conditional denoising diffusion model (CDDM) as the flagship generator, trained via score matching and optionally guided by classifier-free guidance to produce quality event sequences and marks without thinning. The framework is extended with non-parametric KDE and variational CVAE variants, broadening applicability across data regimes, including low- and high-dimensional marks. Empirical results on synthetic, semi-synthetic (image marks), and real data (earthquakes, crime) show superior performance in both generation quality and efficiency, outperforming strong baselines such as DNSK and ETAS. The approach enables thinning-free, scalable modeling of complex spatio-temporal-content dynamics with practical implications for real-time decision-making and downstream analytics.

Abstract

Point processes offer a versatile framework for sequential event modeling. However, the computational challenges and constrained representational power of the existing point process models have impeded their potential for wider applications. This limitation becomes especially pronounced when dealing with event data that is associated with multi-dimensional or high-dimensional marks such as texts or images. To address this challenge, this study proposes a novel event-generation framework for modeling point processes with high-dimensional marks. We aim to capture the distribution of events without explicitly specifying the conditional intensity or probability density function. Instead, we use a conditional generator that takes the history of events as input and generates the high-quality subsequent event that is likely to occur given the prior observations. The proposed framework offers a host of benefits, including considerable representational power to capture intricate dynamics in multi- or even high-dimensional event space, as well as exceptional efficiency in learning the model and generating samples. Our numerical results demonstrate superior performance compared to other state-of-the-art baselines.

Figures (10)

• Figure 1: An example of generating high-dimensional content over time. The conditional generator explores the customer's next possible activity, including not only the purchase time, but also the item, and even its image or review. The observed events from the customer's past purchases are represented by yellow dots, while the next generated event is indicated by a blue dot.
• Figure 2: (a) The architecture of the proposed framework, which consists of two key components: A conditional generative model $g$ that generates $(\Delta \widetilde{t}, \widetilde{m})$ given its history embedding and an RNN-like model $\psi$ that summarizes the events in the history. (b) An example of generated one-dimensional (time only) events $\{\widetilde{x}^{(j)}\}$ given the history $\mathcal{H}_t$. The shaded area suggests the underlying conditional probability density captured by the model parameters $\theta$.
• Figure 3: Out-of-sample estimation of the conditional PDF $f(t|\mathcal{H}_t)$ and the intensity $\lambda(t|\mathcal{H}_t)$ on one-dimensional (time only) synthetic data sets. One sequence is picked from each testing set for evaluation. The grey shaded areas represent the true $f(t|\mathcal{H}_t)$ and the true $\lambda(t|\mathcal{H}_t)$.
• Figure 4: Snapshots of out-of-sample estimation of the conditional PDFs for a three-dimensional (time and space) event sequence, arranged in chronological order from top to bottom. Darker shades indicate higher conditional PDF values. The red dots represent newly observed events, and the circles represent historical events.
• Figure 5: Generated T-MNIST (first row) and T-CIFAR (second row) series using CEG+CDDM and a neural point process baseline DNSK, with true sequences displayed on the left. Each series is generated (blue boxes) given the first two true events (red boxes). Dots on the horizontal lines represent the event times, with dashed lines indicating the association between time and mark.