Beyond Linearity and Time-homogeneity: Relational Hyper Event Models with Time-Varying Non-Linear Effects

2025-09-05

AI Summary

Existing relational hyper-event models (RHEMs) predominantly rely on linear and time-homogeneous assumptions for event-rate modeling, limiting their ability to capture time-varying, nonlinear effects of historical statistics and exogenous covariates. To address this, we propose the first dynamic modeling framework that overcomes these restrictions: it introduces tensor-product smoothing to jointly estimate historical dependencies, exogenous influences, and time-varying nonlinear effects across multi-entity interactions; explicitly models non-monotonic, nonlinear dynamic evolution patterns; and integrates temporal summary construction, nonlinear function estimation, and interpretable learning of time-varying effects. Experiments on synthetic data and a real-world scientific collaboration network demonstrate substantial improvements in predictive accuracy and successfully uncover complex dynamic phenomena—such as evolving collaboration strength and influence diffusion—thereby establishing a novel paradigm for temporal relational event analysis.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Statistical Relational/Logic Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Recent technological advances have made it easier to collect large and complex networks of time-stamped relational events connecting two or more entities. Relational hyper-event models (RHEMs) aim to explain the dynamics of these events by modeling the event rate as a function of statistics based on past history and external information. However, despite the complexity of the data, most current RHEM approaches still rely on a linearity assumption to model this relationship. In this work, we address this limitation by introducing a more flexible model that allows the effects of statistics to vary non-linearly and over time. While time-varying and non-linear effects have been used in relational event modeling, we take this further by modeling joint time-varying and non-linear effects using tensor product smooths. We validate our methodology on both synthetic and empirical data. In particular, we use RHEMs to study how patterns of scientific collaboration and impact evolve over time. Our approach provides deeper insights into the dynamic factors driving relational hyper-events, allowing us to evaluate potential non-monotonic patterns that cannot be identified using linear models.

Problem

• Modeling non-linear time-varying effects in relational hyper-events
• Overcoming linearity limitations in relational event modeling
• Capturing dynamic non-monotonic patterns in network event evolution

Innovation

• Tensor product smooths for joint effects
• Non-linear and time-varying statistical modeling
• Flexible relational hyper-event model dynamics