Stochastic Event Prediction via Temporal Motif Transitions

TL;DR

STEP (STochastic Event Predictor), a framework that reformulates temporal link prediction as a sequential forecasting problem in continuous time, and produces compact, temporal motif-based feature vectors that can be concatenated with existing temporal graph neural network outputs, enriching their representations without architectural modifications.

Abstract

Networks of timestamped interactions arise across social, financial, and biological domains, where forecasting future events requires modeling both evolving topology and temporal ordering. Temporal link prediction methods typically frame the task as binary classification with negative sampling, discarding the sequential and correlated nature of real-world interactions. We introduce STEP (STochastic Event Predictor), a framework that reformulates temporal link prediction as a sequential forecasting problem in continuous time. STEP models event dynamics through discrete temporal motif transitions governed by Poisson processes, maintaining a set of open motif instances that evolve as new interactions arrive. At each step, the framework decides whether to initiate a new temporal motif or extend an existing one, selecting the most probable event via Bayesian scoring of temporal likelihoods and structural priors. STEP also produces compact, temporal motif-based feature vectors that can be concatenated with existing temporal graph neural network outputs, enriching their representations without architectural modifications. Experiments on five real-world datasets demonstrate up to 21% average precision gains over state-of-the-art baselines in classification and 0.99 precision in next $k$ sequential forecasting, with consistently lower runtime than competing motif-aware methods.

Figures (4)

• Figure 1: Examples of motif types in temporal graphs. Event labels represent the temporal order of interactions and nodes are colored distinctly within each motif to indicate uniquness. The six motifs on the left forms the set of 2-event motifs, $\mathcal{M}_2$. The rightmost motifs illustrate an example 3-event and 4-event motif types.
• Figure 2: The operational flow of the Stochastic Event Prediction (STEP) framework. After parameter initialization, the model enters a continuous prediction loop. In each iteration, time advances by $\Delta\tau$, and a Bernoulli decision determines whether to initiate a new motif (Subproblem I) or extend an existing motif (Subproblem II), updating the set of open motifs $\mathbb{O}$ accordingly.
• Figure 3: Precision of STEP sequence forecasting versus the number of predicted events $k$. It remains high near $k=100$ across all five datasets.
• Figure 4: Precision of STEP sequence forecasting as a function of the test ratio, $p\%$ and fixed $k = 100$. Precision improves with larger held‐out fractions and stabilizes beyond 10% in most datasets.

Theorems & Definitions (8)

• definition 1: Temporal Graph
• definition 2: Temporal Motif
• definition 3: Motif Transition
• definition 4: Edge Repetitions and Motif Transition Counts
• definition 5: Motif Transition Process
• definition 6: Cold and Hot Events
• definition 7: Intensity Rate
• definition 8: Open Motif