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# COMPLEX SYSTEMS SEMINAR

Histograms, Graph Limits, and the Asymptotic Behavior of Large Networks

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/).