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SUMMARY:On the Statistical Estimation of the Preferential Attachment Netwo
 rk Model - Fengnan Gao (Universiteit Leiden)
DTSTART:20161216T133000Z
DTEND:20161216T141500Z
UID:TALK69528@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The preferential attachment (PA) network is a popular way of m
 odeling the social networks\, the collaboration networks and etc. The PA n
 etwork model is an evolving network model&nbsp\;where new nodes keep comin
 g in. When a new node comes in\, it establishes only one connection with a
 n existing node. The random choice on the existing node is via a multinomi
 al distribution with probability weights based on a preferential function 
 f on the degrees. f maps the natural numbers to the positive real line and
  is assumed apriori non-decreasing\, which means the nodes with high degre
 es are more likely to get new connections\, i.e. "the rich get richer". We
  proposed an estimator on f. We show\, with techniques from branching proc
 ess\, our estimator is consistent. If f is affine\, meaning f(k) = k + del
 ta\, it is well known that such a model leads to a&nbsp\;power-law degree 
 distribution. We proposed a maximum likelihood estimator for delta and est
 ablish a central limit result on the MLE of delta.&nbsp\; If f belongs to 
 a parametric family no faster than linear\, we show the MLE will also yiel
 d optimal performance with the asymptotic normality results.&nbsp\; We wil
 l also talk about the potential extensions of the model (with borrowed str
 ength from nonparametric Bayesian statistics) and interesting applications
 .&nbsp\;<br>This is joint work with Aad van der Vaart.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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