Estimating the history of a random recursive tree
Machine Learning
2024-12-17 v3 Machine Learning
Social and Information Networks
Abstract
This paper studies the problem of estimating the order of arrival of the vertices in a random recursive tree. Specifically, we study two fundamental models: the uniform attachment model and the linear preferential attachment model. We propose an order estimator based on the Jordan centrality measure and define a family of risk measures to quantify the quality of the ordering procedure. Moreover, we establish a minimax lower bound for this problem, and prove that the proposed estimator is nearly optimal. Finally, we numerically demonstrate that the proposed estimator outperforms degree-based and spectral ordering procedures.
Cite
@article{arxiv.2403.09755,
title = {Estimating the history of a random recursive tree},
author = {Simon Briend and Christophe Giraud and Gábor Lugosi and Déborah Sulem},
journal= {arXiv preprint arXiv:2403.09755},
year = {2024}
}