on the consistency of estimating the preferential attachment function

ON THE CONSISTENCY OF ESTIMATING THE
PREFERENTIAL ATTACHMENT FUNCTION AND THE
ASYMPTOTIC NORMALITY OF ESTIMATING THE AFFINE
PREFERENTIAL PARAMETER
Soumis par : Fengnan Gao
Type de résumé : Présentation orale
Session : Lundi 31/08 : EXPOSES, SESSION 1
Auteur Orateur : Fengnan Gao and Aad van der Vaart
Liste complète des auteurs - Affiliations :
Aad van der Vaart http://www.math.leidenuniv.nl/~avdvaart/info.html
Aad van der Vaart (born 1959) is a Dutch professor of Stochastics at the
Mathematical Institute of Leiden University. He has been member of the
Royal Netherlands Academy of Arts and Sciences since 2009.[1]
Résumé :
Preferential attachment model (PAM), first introduced by is a popular way
of modeling the social networks, the collaboration networks and etc. PAM
is an evolving network where new nodes keep coming in. When a new
node comes in, it establishes only one connection with an existing node.
The random choice on the existing node is via a multinormial distribution
with probability weights based on a preferential function f on the degrees. f
is assumed apriori nondecreasing, which means the nodes with high
degrees are more likely to get new connections, i.e. "the rich get richer".
We proposed an estimator on f, that maps the natural numbers to the
positive real line. We show, with techniques from branching process, our
estimator is consistent. If f is affine, meaning f(k) = k + delta, it is well
known that such a model leads to a power-law degree distribution. We
proposed a maximum likelihood estimator for delta and establish a central
limit result on the MLE of delta.
Simulation results will also be shown.
Références bibliographiques : Selected
Reference
Van Der Hofstad, R. (2009). Random graphs and complex networks.
Available on http://www.win.tue.nl/rhofstad/NotesRGCN. pdf.
Barabási, Albert-László, and Réka Albert. "Emergence of scaling in
random networks." science 286, no. 5439 (1999): 509-512.
Rudas, Anna, Bálint Tóth, and Benedek Valkó. "Random trees and general
branching processes." Random Structures & Algorithms 31, no. 2 (2007):
186-202.
Móri, T. "On random trees." Studia Scientiarum Mathematicarum
Hungarica 39, no. 1-2 (2002): 143-155.
Mots clés : networks high_dimensional_statistics power_law
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