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Histograms, graph limits, and the asymptotic behavior of large networks

Tuesday, April 22, 2014
12:00 AM
4448 East Hall

Abstract: In this talk - which will be accessible to a general audience -
we show how the asymptotic behavior of large networks can be exploited for
nonparametric statistical inference, using recent developments from the
theory of graph limits and the corresponding analog of de Finetti's
theorem.  We introduce the notion of a network histogram, obtained by
fitting a stochastic blockmodel to a single observation of a network
dataset.  Blocks of edges play the role of histogram bins, and community
sizes that of histogram bandwidths or bin sizes.  Working within the
framework of exchangeable arrays subject to bond percolation, we prove
consistency of network histogram estimation under general conditions,
giving rates of convergence which include the important practical setting
of sparse networks.

Joint work with David Choi (http://arxiv.org/abs/1212.4093) and Sofia
Olhede (http://arxiv.org/abs/1309.5936/, http://arxiv.org/abs/1312.5306/).

Speaker:
Patrick Wolfe, University College London