Estimating the history of a random recursive tree
<|reference_start|>Estimating the history of a random recursive tree: 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.<|reference_end|>
@article{briend2024estimating,
    title={Estimating the history of a random recursive tree},
    author={Simon Briend, Christophe Giraud, G'abor Lugosi and D'eborah Sulem},
    journal={arXiv preprint arXiv:2403.09755},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.09755},
    primaryClass={stat.ML cs.LG cs.SI}
}