Peter Bickel Inference for unlabelled graphs
In view of the emergence of dense networks such as the Internet, and manifestations such as Facebook, a great deal of attention has recently been given to unlabelled graphs possibly with covariates.
A heavily studied problem has been the identification of communities of individuals,
corresponding to vertices of an unlabelled graph. A description of these and other
problems may be found in the recent monographs of Newman (2010), Kleinberg et al.
(2010) and Kolaczyc (2010). There is a well developed inference literature in the
social sciences, see Wasserman and Faust (1994) but the network sizes addressed tend
to be small. Chen and I recently introduced a nonparametric framework for probabilistic
ergodic models of infinite unlabelled graphs (PNAS2009) and made some connections with
modularities arising in the physics literature and community models in the social
sciences. Our hope is to develop exploratory and confirmatory methods in this framework
which have the power of clarifying and testing parametric assumptions in this complex
setting that their analogues have in the study of models for samples of independent
observations. We will advance and give some results on methods we have developed for
both dense and sparse graphs.
(This is joint work with Aiyou Chen, Liza Levina,and Sharmodeep Bhattacharyya)