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On the Statistical Estimation of the Preferential Attachment Network Model

Presented by: 
Fengnan Gao Universiteit Leiden
Friday 16th December 2016 - 13:30 to 14:15
INI Seminar Room 1
The preferential attachment (PA) network is a popular way of modeling the social networks, the collaboration networks and etc. The PA network model is an evolving network model 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 multinomial 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 degrees 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 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.  If f belongs to a parametric family no faster than linear, we show the MLE will also yield optimal performance with the asymptotic normality results.  We will also talk about the potential extensions of the model (with borrowed strength from nonparametric Bayesian statistics) and interesting applications. 
This is joint work with Aad van der Vaart. 
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons