This work proposes a general framework for model selection in binary-state spreading processes on networks and shows that asymptotic approximations in the thermodynamic limit can accurately predict inference outcomes in finite systems.
Abstract
Mechanisms of interaction in spreading models are central to our quantitative understanding of networked contagion processes, from disease transmission to opinion dynamics. Yet, while empirical data can reveal who interacts with whom, they rarely provide direct information about how interactions drive spreading, leaving the underlying mechanism to be inferred from observed dynamics, and selected among competing hypotheses. We propose a general framework for model selection in binary-state spreading processes on networks and show that asymptotic approximations in the thermodynamic limit can accurately predict inference outcomes in finite systems. By systematically exploring a broad parameter space, we characterize the detectability of six archetypal spreading mechanisms commonly used in the literature and find that accuracy generally increases in sparse networks, which are prevalent in real-world systems, and near phase transitions, such as the epidemic threshold of simple contagion processes. We further assess the prevalence of these mechanisms across a diverse set of empirical datasets, highlighting the impact of data preprocessing on model recovery. Our results show that statistical model selection can fail under common conditions and suggest new directions for overcoming these limitations.
A cascade over a network refers to the diffusion process where behavior changes occurring in one part of an interconnected population lead to a series of sequential changes throughout the entire population. In recent years, there has been a surge in interest and efforts to understand and model cascade mechanisms since they motivate many significant research topics across different disciplines. The propagation structure of cascades is governed by underlying diffusion networks that are often hidden. Inferring diffusion networks thus enables interventions in cascading process to maximize information propagation and provides insights into the Granger causality of interaction mechanisms among individuals. In this project, we propose a novel double network mixture model for inferring latent diffusion network in presence of strong cascade heterogeneity. The new model represents cascade pathways as a distributional mixture over diffusion networks that capture different cascading patterns at the population level. We develop a data-driven optimization method to infer diffusion networks using only visible temporal cascade records, avoiding the need to model complex and heterogeneous individual states. Both statistical and computational guarantees are established for the proposed method. We apply the proposed model to analyze research topic cascades in social sciences across U.S. universities and uncover the latent research topic diffusion network among top U.S. social science programs.
Siyu Huang, Yubai Yuan, A. Adeel· Neural Information Processin...· 0 citations
The simulation of rare macroscopic events in stochastic network dynamics, such as widespread epidemic outbreaks, cascading failures in communication networks, or the escape from metastable states in many-body systems, is severely hindered by methodological challenges like catastrophic rejection rates, weight degeneracy, genealogical correlations, and critical slowing down inherent to standard forward-time algorithms, splitting methods, and transition-path sampling. Conditional-path Monte Carlo (CPMC) overcomes these limitations by employing non-local Swendsen-Wang-like cluster updates that operate directly on full-system trajectories. Serving as the technical companion to [Sun, Moody, and Barthel, arXiv:2608.16171], this paper provides the rigorous mathematical foundations and algorithmic details underlying the CPMC framework. We formally define the joint path-graph probability weights and derive the transition and uniformization sum rules that guarantee detailed balance. Applying the framework to susceptible-infectious-susceptible (SIS) models, we systematically construct and optimize single-node and edge graph vertex sets specifically designed to prevent lock avalanches and maintain the structural mobility of the epidemic trunk. Furthermore, we detail a dynamic programming scheme to exactly implement complex boundary conditions - including patient-zero and macroscopic outbreak-size constraints - enabling the rejection-free generation of valid trajectories. Finally, we assess the computational complexity of the algorithm, describe parallelization strategies, and validate CPMC against exact solutions for dynamics on small networks.
Thomas Barthel, Jiazheng Sun, Jhao-Hong Peng· 1 citation
Understanding the stochastic evolution in complex networks is a central challenge across physics, biology, engineering, social science, and finance. The most consequential macroscopic events, like cascading failures in communication networks, widespread epidemic outbreaks, and rapid shifts in societal opinions, often emerge from a confluence of rare, localized stochastic processes and need to pass certain bottlenecks. Standard forward-time simulation algorithms like the Gillespie method are inefficient for the investigation of such phenomena due to catastrophic rejection rates. Advanced rare-event techniques like splitting methods and transition-path sampling often suffer from kinetic trapping, path degeneracy, genealogical correlations, or critical slowing down when applied to complex heterogeneous networks. We propose to overcome this challenge by establishing a novel technique called conditional-path Monte Carlo (CPMC), inspired by loop algorithms from equilibrium condensed-matter physics. By employing non-local updates on spacetime clusters without rejections, CPMC generates a Markov chain of trajectories that all strictly respect the targeted macroscopic boundary conditions like the occurrence of a massive network failure. We demonstrate the framework's potential by performing a simple risk factor analysis for rare large-scale epidemic outbreaks in SIS dynamics on kinship networks.
Jiazheng Sun, J. Moody, Thomas Barthel· 1 citation
This work proposes a community-based preferential attachment hypergraph model with tunable modularity and a heavy-tailed degree distribution, reproducing key structural properties in real systems, and develops a hypergraph-based SAIR framework to describe epidemic dynamics with asymptomatic transmission.
A unified complete-data likelihood framework for epidemic processes evolving on partially observed dynamic networks that contributes to statistical inference for partially observed interacting stochastic systems on evolving networks and establishes a foundation for uncertainty-aware analysis of complex transmission processes.
