🤖 AI Summary
This work addresses nonparametric modeling of temporal networks exhibiting dynamic features such as memory and periodicity, while preserving node exchangeability. To this end, the authors propose a unified framework based on dynamic decorated graphons, decomposing the modeling task into two stages: temporal process modeling and network structure estimation. This approach is the first to accommodate complex temporal dependencies under the constraint of exchangeability, offering rigorous nonparametric convergence rate guarantees. By integrating block models with a two-stage estimator under Hölder smoothness assumptions on the temporal dynamics, the method accommodates diverse edge evolution processes, including autoregressive and Markovian structures. Experiments on both synthetic data and a real-world hospital contact network successfully recover latent community structures and time-varying interaction patterns, demonstrating the method’s empirical effectiveness and theoretical soundness.
📝 Abstract
We propose a unified nonparametric framework for modeling time-evolving networks using decorated graphons (also known as probability-graphons): symmetric functions that assign to each node pair a probability distribution over binary edge time series. This generalizes the static decorated-graphon construction to dynamic graphs while preserving node exchangeability and allowing temporal dynamics such as memory and periodicity. Models in which edges evolve independently given the latent variables, such as autoregressive and Markov edge processes, arise as special cases. We develop a two-stage estimation procedure that separates temporal modeling from network structure. Because the network stage requires only mild regularity conditions on the edge-process estimator, a broad class of temporal edge models can be used in the first stage. We establish nonparametric convergence rates in both block-model and Hölder-smooth regimes, and make explicit how the rate depends on the number of observed time steps and on the quality of the edge-level estimation. We illustrate the method on simulated data and a hospital contact network, recovering latent community structure and time-varying interaction patterns. The framework gives a nonparametric baseline for dynamic network analysis with explicit convergence guarantees.