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SUMMARY:Histograms\, Graph Limits\, and the Asymptotic Behavior of Large N
 etworks - Sofia Olhede\, University College London
DTSTART:20140516T150000Z
DTEND:20140516T160000Z
UID:TALK52255@talks.cam.ac.uk
CONTACT:20082
DESCRIPTION:Networks are fast becoming part of the modern statistical land
 scape. Yet we lack a full understanding of their large-sample properties i
 n all but the simplest settings. This is hindering the development of mode
 ls and estimation methods that admit theoretical performance guarantees. T
 he asymptotic behavior of large networks can be exploited for nonparametri
 c statistical inference\, using recent developments from the theory of gra
 ph limits\, and the corresponding analog of de Finetti's theorem.\n\n\nA n
 etwork histogram is obtained by fitting a stochastic blockmodel to a singl
 e observation of a network dataset. Blocks of edges play the role of histo
 gram bins\, and community sizes that of histogram bandwidths or bin sizes.
  Just as standard histograms allow for varying bandwidths\, different bloc
 kmodel estimates can all be considered valid representations of an underly
 ing probability model\, subject to bandwidth constraints. We show that und
 er these constraints\, the mean integrated square error of the network his
 togram tends to zero as the network grows large\, and we provide methods f
 or optimal bandwidth selection-thus making the blockmodel a universal repr
 esentation. With this insight\, we discuss the interpretation of network c
 ommunities in light of the fact that many different community assignments 
 can all give an equally valid representation of the network.\n\n\nTo demon
 strate the fidelity-versus-interpretability tradeoff inherent in consideri
 ng different numbers and sizes of communities\, we show an example of dete
 cting and describing new network community microstructure in political web
 log data. \n\n\nThis is joint work with Patrick Wolfe - UCL​\n
LOCATION:MR12\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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