通过随机环境关联，用轨迹数据估算边增强随机游走的初始边权。
On Statistical Estimation of Edge-Reinforced Random Walks
- 基于广义矩估计法，利用随机环境等价关系设计新估计算法。
- 在双曲高斯结构下，严格界定了参数估计的样本复杂度。
- 适用于网络建模与动物行为分析中的动态路径学习场景。
边增强随机游走（ERRW）是根据历史访问记录动态调整转移概率的随机过程，已应用于网络表征学习、强化版PageRank及动物行为建模等领域。然而，其参数的统计估计仍缺乏系统研究。本文聚焦于从观测轨迹中估计ERRW的初始边权重。借助ERRW与随机环境中随机游走（RWRE）之间的“魔法公式”联系，提出一种基于广义方法的矩估计器。为分析该估计器的样本复杂度，利用随机环境中嵌入的双曲高斯结构，对底层随机边电导率的波动进行上界控制。
原文摘要 · Abstract (English)
Reinforced random walks (RRWs), including vertex-reinforced random walks (VRRWs) and edge-reinforced random walks (ERRWs), model random walks where the transition probabilities evolve based on prior visitation history~\cite{mgr, fmk, tarres, volkov}. These models have found applications in various areas, such as network representation learning~\cite{xzzs}, reinforced PageRank~\cite{gly}, and modeling animal behaviors~\cite{smouse}, among others. However, statistical estimation of the parameters governing RRWs remains underexplored. This work focuses on estimating the initial edge weights of ERRWs using observed trajectory data. Leveraging the connections between an ERRW and a random walk in a random environment (RWRE)~\cite{mr, mr2}, as given by the so-called ``magic formula", we propose an estimator based on the generalized method of moments. To analyze the sample complexity of our estimator, we exploit the hyperbolic Gaussian structure embedded in the random environment to bound the fluctuations of the underlying random edge conductances.
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