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Multivariate power laws in a preferential attachment network model; model calibration

Presented by: 
Sidney Resnick Cornell University, Cornell University
Wednesday 14th December 2016 - 16:00 to 16:45
INI Seminar Room 1

We begin with a review of the multivariate regular variation of in- and out-degree in a preferential attachment model. The problem can be approached in a variety of ways: (i) Multivariate Tauberian theory; (ii) Direct approach via asymptotics to get a limit measure; (iii) proving multivariate regular variation of the limiting mass function of normalized in- and out-degree. We then turn to model calibration comparing various information sources and methods. If a full history of network growth is available, full MLE implementation is possible and performs well on simulated data. If a single snapshot in time is all that is available, then approximate MLE can be used. Comparison with MLE and use of asymptotic methods relying on heavy tail estimators is also made and predictably there is a trade-off between robustness and accuracy. Methods generally perform well on simulated data but real data creates problems with model error and we can illustrate this with wikipedia data obtained from Konect.

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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons