The framework gives a nonparametric baseline for dynamic network analysis with explicit convergence guarantees and establishes nonparametric convergence rates in both block-model and Holder-smooth regimes.
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 H\"older-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.
Understanding how links form and predicting future link states is of great importance in social, traffic, and many other complex temporal networks. These temporal networks are typically governed by multiple evolutionary mechanisms. However, existing dynamic graph representation methods, especially dynamic graph neural networks (DGNNs), are constrained by their single-evolutionary-path architecture, where spatial and temporal dynamics are either sequentially stacked or integrated into a monolithic module in a fixed manner. This design not only restricts the exploration of diverse evolutionary paths arising from rich evolutionary mechanisms but also confines spatiotemporal interactions to passive and implicit modeling, resulting in compromised performance and weak interpretability. To address these issues, we propose a novel theoretical model, namely the multiway autoregressive (MARS) model, which characterizes multiple evolutionary paths by capturing dependencies within and across two core factors underlying diverse evolutionary mechanisms. Based on this theoretical foundation, we develop a general DGNN framework, a multiway autoregressive network (MAN), by transforming the network architecture into a 2-D diagram that characterizes evolutionary dependencies in the spatiotemporal domain. Each node encodes an evolving state of the dynamic graph representation, while each edge denotes an evolutionary transition from one state to another. Moreover, three elementary evolutionary operators are incorporated into edges along distinct directions, capturing spatialwise, temporalwise, and cross-spatiotemporal evolutionary dynamics, respectively. This enables researchers to develop a variety of DGNNs by configuring the evolutionary operators in different ways. To validate the effectiveness of this framework, we design a new DGNN, which employs a graph convolutional network (GCN), a gated recurrent unit (GRU), and our proposed time-delayed GCN (TD-GCN) as core components. Promising experimental results demonstrate that the proposed approach achieves state-of-the-art temporal link prediction performance on both synthetic and real-world temporal networks across diverse domains.
Ping He, Xiao-hua Xu· IEEE Transactions on Neural...· 0 citations
Graph signal processing provides a powerful framework for analyzing data defined over irregular network structures. Estimation of effective models from a set of timevarying graph signals requires capturing both temporal dynamics and graph-dependent statistical structures. Existing approaches that model time-vertex signals as stochastic processes typically assume a globally stationary model, which often fails to represent local variations that naturally arise across both temporal and graph dimensions. In this work, we address the problem of learning parametric models for graph signals exhibiting locally stationary behavior over time and graph. We propose a locally stationary time-vertex signal model that extends stationarity to a locally adaptive setting and develop an algorithm to learn the model parameters. Experiments on synthetic and real datasets demonstrate improved estimation accuracy over existing time-vertex methods.
Deniz Aslan, Elif Vural· Signal Processing and Commun...· 0 citations
A fuzzy network jump model for clustering time-varying observations indexed by the nodes of a weighted graph that accurately recovers the true membership probabilities and outperforms competing clustering methods is introduced.
By specifying a stochastically evolving hidden Markov network model, this work addresses two important directions for further investigation identified by Chang et al. (2022): robustness to non-identical network replicates, and efficient aggregation of multiple available network snapshots.
Temporal graphs are increasingly used to model dynamic systems in diverse domains such as social networks, financial networks, and traffic networks. Predicting both what the next event will be and when it will occur in these systems is crucial for understanding and anticipating complex behaviors, but has not been studied much. To address this gap, we propose a unified mathematical framework capable of capturing varying degrees of complexity across temporal graphs. Our framework is flexible and expressive enough to accommodate a wide range of network structures and temporal dynamics. Building upon this analysis, we introduce our novel approach for jointly predicting the next event and its occurrence time. Empirical evaluations across multiple datasets demonstrate that our method consistently outperforms existing techniques, particularly in scenarios involving irregular event patterns and complex temporal dependencies. These findings highlight the potential of our framework as a robust foundation for future research in temporal event prediction.
Mohammad Ostadmohammadi, Sepehr Kazemi, Hamid R. Rabiee· 0 citations
The proposed method, TRicci, extends classical Forman-Ricci curvature to directed weighted temporal graphs by capturing structural support, temporal recency, and local interaction competition and suggests that temporal curvature can serve as a principled basis for scalable temporal graph learning by preserving predictive temporal-structural information under substantial sparsification.
Poupak Azad, C. Akcora, Kiarash Shamsi· 0 citations