arXiv subjects

Alexander Fuchs-Kreiss

Publications and source records attributed to Alexander Fuchs-Kreiss.

3 recordsLinked to original sources

arXiv2026

Common Drivers in Sparsely Interacting Hawkes Processes

We study a multivariate Hawkes process as a model for time-continuous relational event networks. The model does not assume the network to be known, it includes covariates, and it allows for both common drivers, parameters common to all the actors in the network, and also local parameters specific for each actor. We derive rates of convergence for all of the model parameters when both the number of actors and the time horizon tends to infinity. To prevent an exploding network, sparseness is assumed. We also discuss numerical aspects.

math.ST↗

arXiv2026

A Counting Process View of Relational Event Models: Practical Asymptotics

Relational Event Models (REMs) provide a rigorous framework for analyzing dyadic interactions observed in continuous time, capturing history-dependent dynamics such as triadic closure and reciprocity. Framing REMs through the lens of counting processes embeds the model in a rich theoretical foundation, facilitating its mathematical analysis. While Maximum Likelihood Estimation (MLE) is standard practice for estimating these models, the underlying statistical guarantees rely on specific asymptotic regimes, namely, whether the network size (n), the observational period (T), or both approach infinity. We review the theoretical foundations of such counting-process-based models, formalizing the core assumptions required to achieve asymptotic normality across these different limits. With a specific focus on Cox-type multiplicative models, we detail the circumstances under which these assumptions hold. Supported by simulation studies, we illustrate how structural modeling choices, including temporal windowing and logarithmic transformations, affect empirical coverage and estimator convergence. We thereby derive several guiding principles for specifying such models in realistic contexts, bridging theory and practice.

stat.ME↗

arXiv2025

Testing for correlation between network structure and high-dimensional node covariates

In many application domains, networks are observed with node-level features. In such settings, a common problem is to assess whether or not nodal covariates are correlated with the network structure itself. Here, we present four novel methods for addressing this problem. Two of these are based on a linear model relating node-level covariates to latent node-level variables that drive network structure. The other two are based on applying canonical correlation analysis to the node features and network structure, avoiding the linear modeling assumptions. We provide theoretical guarantees for all four methods when the observed network is generated according to a low-rank latent space model endowed with node-level covariates, which we allow to be high-dimensional. Our methods are computationally cheaper and require fewer modeling assumptions than previous approaches to network dependency testing. We demonstrate and compare the performance of our novel methods on both simulated and real-world data.

stat.ML↗