ResearchTrend.AI
  • Papers
  • Communities
  • Events
  • Blog
  • Pricing
Papers
Communities
Social Events
Terms and Conditions
Pricing
Parameter LabParameter LabTwitterGitHubLinkedInBlueskyYoutube

© 2025 ResearchTrend.AI, All rights reserved.

  1. Home
  2. Papers
  3. 1712.01745
65
3
v1v2v3 (latest)

An estimator for the tail-index of graphex processes

5 December 2017
Zacharie Naulet
Daniel M. Roy
Ekansh Sharma
Victor Veitch
ArXiv (abs)PDFHTML
Abstract

Graphex processes resolve some pathologies in traditional random graph models, notably, providing models that are both projective and allow sparsity. In a recent paper, Caron and Rousseau (2017) show that for a large class of graphex models, the sparsity behaviour is governed by a single parameter: the tail-index of the function (the graphon) that parameterizes the model. We propose an estimator for this parameter and quantify its risk. Our estimator is a simple, explicit function of the degrees of the observed graph. In many situations of practical interest, the risk decays polynomially in the size of the observed graph. We illustrate the importance of a good estimator for the tail-index through the graph analogue of the unseen species problem. We also derive the analogous results for the bipartite graphex processes.

View on arXiv
Comments on this paper