Title: Maximum likelihood estimation of preferential attachment network models
Authors: Fengnan Gao - Fudan University and SCMS (China) [presenting]
Abstract: 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 a priori non-decreasing, which means the nodes with high degrees are more likely to get new connections, i.e. ``the rich get richer''. If $f$ is affine with $f(k) = k + \delta$, 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 consider the potential extensions of the model (with borrowed strength from nonparametric Bayesian statistics) and interesting applications.