AI 中文总结
提出用装饰图子建模时间演化网络的统一非参数框架，开发两阶段估计程序分离时间建模与网络结构，建立非参数收敛速率，在模拟数据和医院接触网络上验证，为动态网络分析提供非参数基线。
AI 中文摘要
我们提出了一个统一的非参数框架，使用装饰图子（也称为概率图子）对随时间演化的网络进行建模：对称函数为每个节点对分配二元边时间序列上的概率分布。这将静态装饰图子构造推广到动态图，同时保留节点可交换性并允许诸如记忆和周期性等时间动态。给定潜在变量时边独立演化的模型，如自回归和马尔可夫边过程，是特殊情况。我们开发了一种两阶段估计程序，将时间建模与网络结构分离。网络阶段对边过程估计器仅需温和的正则条件，第一阶段可使用广泛的时间边模型。我们在块模型和赫尔德平滑区域建立了非参数收敛速率，并明确速率如何依赖于观测时间步长数量和边级估计质量。我们在模拟数据和医院接触网络上说明了该方法，恢复了潜在社区结构和随时间变化的交互模式。该框架为动态网络分析提供了具有明确收敛保证的非参数基线。
英文摘要
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.
