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

arXiv: https://arxiv.org/abs/2509.05289 · HTML: https://mlsanity.com/paper/2509.05289/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 52 references that are in the map.
- First posted on arXiv 5 Sep 2025.

## Builds on (most cited first, 10 of 10)

- [Motifs in Temporal Networks](https://mlsanity.com/paper/1612.09259/) (2016)
- [Forgotten Knowledge: Examining the Citational Amnesia in NLP](https://mlsanity.com/paper/2305.18554/) (2023)
- [Efficient Sampling Algorithms for Approximate Temporal Motif Counting (Extended Version)](https://mlsanity.com/paper/2007.14028/) (2020)
- [Dynamic latent space relational event model](https://mlsanity.com/paper/2204.04753/) (2022)
- [Reliability of relational event model estimates under sampling: how to fit a relational event model to 360 million dyadic events](https://mlsanity.com/paper/1905.00630/) (2019)
- [Modeling non-linear Effects with Neural Networks in Relational Event Models](https://mlsanity.com/paper/2312.12357/) (2023)
- [Relational hyperevent models for polyadic interaction networks](https://mlsanity.com/paper/2112.10552/) (2021)
- [Relational hyperevent models for the coevolution of coauthoring and citation networks](https://mlsanity.com/paper/2308.01722/) (2023)
- [What Large-Scale Publication and Citation Data Tell Us About International Research Collaboration in Europe: Changing National Patterns in Global Contexts](https://mlsanity.com/paper/2402.09407/) (2023)
- [Goodness of fit of relational event models](https://mlsanity.com/paper/2407.08599/) (2024)

## Abstract (arXiv)

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.