发表机构
Imperial College London（帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种结合随机块模型的网络泊松自回归框架，证明平均场近似的收敛性，并将参数推断复杂度从O(N^2T^2)降至O(NT^2)。
AI 中文摘要
我们考虑在由随机块模型生成的随机网络上演化的多元泊松自回归过程。该框架通过纳入潜在社区结构并允许非马尔可夫依赖（既包括兴奋性也包括抑制性）来扩展现有的网络泊松自回归。我们建立了平均场近似，并证明在淬火设置中，有限系统以最优速率$N^{-1/2}$收敛到其极限，且具有压倒性概率，无论是在平均意义下还是在一致范数下。我们的分析产生了在时间范围上显式的定量误差界，并且在适当的稳定性条件下，这些误差界随时间保持多项式或一致，从而避免了通常与Grönwall型论证相关的指数增长。因此，平均场近似被证明在任何时间范围上一致成立。我们进一步展示了如何利用该近似将参数推断的计算复杂度从$\mathcal{O}(N^2T^2)$降低到$\mathcal{O}(NT^2)$。这些结果为具有社区结构的大型随机网络上计数型过程的分析和推断提供了理论基础。
英文摘要
We consider multivariate Poisson autoregressive processes evolving on random networks generated by a Stochastic Block Model. This framework extends existing network Poisson autoregressions by incorporating latent community structure and allowing for non-Markovian dependence, both excitatory and inhibitory. We establish a mean-field approximation and prove that the finite system converges to its limit at the optimal rate $N^{-1/2}$ in the quenched setting with overwhelming probability, both on average and in uniform norm. Our analysis yields quantitative error bounds that are explicit in the time horizon and, under suitable stability conditions, remain polynomial or uniform in time, thereby avoiding the exponential growth typically associated with Grönwall-type arguments. As a consequence, the mean-field approximation is shown to hold uniformly over any time horizon. We further demonstrate how the approximation can be exploited to reduce the computational complexity of parametric inference from $\mathcal{O}(N^2T^2)$ to $\mathcal{O}(NT^2)$. The results provide a theoretical foundation for the analysis and inference of count-valued processes on large random networks with community structure.
