This talk looks at how the parameters of a complex network model may be estimated. Specifically, I examine the application of Approximate Bayes Computation as an alternative to likelihood or link based techniques. In the general area of model fitting, likelihood/Bayesian based approaches are popular not just because of the excellent parameter estimates but also because they return the posterior distribution of the parameter -- i.e. we can see how probable it is that a parameter actually has a different value from the one we are using. One can think for example of the case where the posterior is almost uniform which essentially means the parameter estimate is useless; in this case care should be taken when deriving conclusions from the model. Approximate Bayesian Computation (ABC) is a method for estimating the posterior distribution for model parameters when the a likelihood based approach doesn't work; typically this occurs when the likelihood function a) doesn't exist, b) the likelihood is vanishingly small or c) it is just too complicated or time consuming to derive (especially if one is not convinced the model is appropriate in the first case). ABC has been around for many years but has recently become very popular due to some advances in the "summary statistic selection problem" -- the Achilles heal of ABC. It may come as a surprise that 11 years after the introduction of the preferential attachment model there still exists no likelihood expression for that model. For the small world model one can only place bounds on the parameters. For models that include anything of greater complexity one is left without any option. This research thus asks the question, can ABC be applied to any graph topology generator? We then look at the answer and uncover some interesting technical issues leading to a set of heuristics for using ABC. We also take some real world data sets and show how using ABC we can select appropriate models for those datasets.
Damien Fay obtained a B.Eng from UCD (1995), an MEng (1997) and PhD (2003) from DCU and worked as a mathematics lecturer at the National University of Ireland (2003-2007) before joining the NetOS group, Computer Laboratory, Cambridge from 2008-2010 as a research associate. He was a research fellow at the Cork centre for computational complexity, 4C, University College Cork from 2011-2012. Damien recently took up a tenured lectureship in big data analysis with the smart technologies research centre at Bournemouth university. Damien is best known for developing the wavelet transfer model in time series analysis, the weighted spectral distribution metric in applied graph theory and recently lodged a patent for an arrival time prediction algorithm which has won a UCC commercialisation 2012 award. His interests are in the areas of time series analysis and applied graph theory.