The network histogram, nonparametric function estimation, and graph limits

In this talk we show how the limiting behavior of large networks can be exploited for nonparametric statistical inference. 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/).