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On Statistical Estimation of Edge-Reinforced Random Walks
Qinghua (Dev · 2026-05-23 · via cs.LG updates on arXiv.org

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Abstract: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.
Comments: This is the full version of the conference paper in submission to ISIT 2025
Subjects: Machine Learning (stat.ML); Information Theory (cs.IT); Machine Learning (cs.LG); Probability (math.PR)
Cite as: arXiv:2503.06115 [stat.ML]
  (or arXiv:2503.06115v2 [stat.ML] for this version)
  https://doi.org/10.48550/arXiv.2503.06115

arXiv-issued DOI via DataCite

Submission history

From: Qinghua (Devon) Ding [view email]
[v1] Sat, 8 Mar 2025 07:57:50 UTC (41 KB)
[v2] Thu, 21 May 2026 00:31:37 UTC (49 KB)