Higher-Order Temporal Network Prediction and Interpretation

TL;DR

This work tackles predicting higher-order temporal network interactions by introducing memory-based prediction frameworks that operate one time step ahead on hyperlink activity. It advances from a baseline that rewrites higher-order events as pairwise interactions to a generalized model that aggregates neighbor-type memory with exponential decay, and finally to a refined model that emphasizes sub- and super-neighbors based on observed correlations and coefficient analyses, with coefficients learned via Lasso. Across eight real-world datasets, both generalized and refined approaches outperform the baseline, with the refined method particularly effective for orders $2$ and $3$, and robust performance for higher orders given appropriate data, memory length $L$, and decay $\tau$. The study also quantitatively links past target activity and its overlap with neighboring groups to predictive power, providing insights into which network mechanisms most drive higher-order event forecasting and interpretation. These results have practical implications for forecasting information spread, epidemics, and opinion dynamics in social systems where group interactions dominate.

Abstract

A social interaction (so-called higher-order event/interaction) can be regarded as the activation of the hyperlink among the corresponding individuals. Social interactions can be, thus, represented as higher-order temporal networks, that record the higher-order events occurring at each time step over time. The prediction of higher-order interactions is usually overlooked in traditional temporal network prediction methods, where a higher-order interaction is regarded as a set of pairwise interactions. The prediction of future higher-order interactions is crucial to forecast and mitigate the spread the information, epidemics and opinion on higher-order social contact networks. In this paper, we propose novel memory-based models for higher-order temporal network prediction. By using these models, we aim to predict the higher-order temporal network one time step ahead, based on the network observed in the past. Importantly, we also intent to understand what network properties and which types of previous interactions enable the prediction. The design and performance analysis of these models are supported by our analysis of the memory property of networks, e.g., similarity of the network and activity of a hyperlink over time respectively. Our models assume that a target hyperlink's future activity (active or not) depends the past activity of the target link and of all or selected types of hyperlinks that overlap with the target. We then compare the performance of both models with a baseline utilizing a pairwise temporal network prediction method. In eight real-world networks, we find that both models consistently outperform the baseline and the refined model tends to perform the best. Our models also reveal how past interactions of the target hyperlink and different types of hyperlinks that overlap with the target contribute to the prediction of the target's future activity.

Figures (10)

• Figure 1: Average number of $\phi$-neighbors per hyperlink, including error bars, for every dataset.
• Figure 2: Jaccard similarities $J_d(\Delta)$ of eight real-world physical contact networks for events of order $d \in [2,5]$ as a function of the time lag $\Delta$.
• Figure 3: The average auto-correlations $R_{i,i}(\Delta)$ of the activity of an order $d$ hyperlink as a function of the time lag $\Delta$ in each real-world physical contact network.
• Figure 4: Average Pearson correlation coefficient $R_{i,\phi}(\Delta)$ for order $3$ hyperlinks in eight real-world physical contact networks as a function of time lag $\Delta$.
• Figure 5: Prediction accuracy of order $3$ events in the refined model as a function of $c_{322}$, with $c_{343}$ fixed, for all datasets.