366421f798405410VgnVCM100000c2b1d38dRCRDapproved/UMICH/stats/Home/News & Events/Statistics SeminarJoint Seminar with The Center For The Study Of Complex Systems: Patrick Wolfe, Histograms, Graph Limits, and the Asymptotic Behavior of Large Networks###@###(Tue, 22 Apr 2014)Joint Seminar with The Center For The Study Of Complex Systems: Patrick Wolfe, Histograms, Graph Limits, and the Asymptotic Behavior of Large Networks###@###(Tue, 22 Apr 2014)4448 East Hallcscs1398182400000139818240000012:00 PM<p style=" font-family: 'Times New Roman', serif; font-size: 12.0pt; margin-right: 0in; margin-left: 0in;"><span style=" background: white; color: #222222; font-size: medium;">Abstract: &nbsp;In this talk - which will be accessible to a general audience -</span><span style=" font-size: medium;">we show how the asymptotic behavior of large networks can be exploited for<span style=" color: #222222; font-size: medium;"> <span style=" background: white; color: #222222; font-size: medium;">nonparametric statistical inference, using recent developments from the</span></span> <span style=" font-size: medium; background: white;">theory of graph limits and the corresponding analog of de Finetti's </span><span style=" text-align: start; background: white; word-spacing: 0px; orphans: auto; float: none; -webkit-text-stroke-width: 0px; font-size: medium; widows: auto;">theorem. &nbsp;We introduce the notion of a network histogram, obtained by</span> <span style=" font-size: medium; background: white;">fitting a stochastic blockmodel to a single observation of a network</span> <span style=" font-size: medium; background: white;">data set. &nbsp;Blocks of edges play the role of histogram bins, and community</span> <span style=" font-size: medium; background: white;">sizes that of histogram bandwidths or bin sizes. &nbsp;Working within the</span> <span style=" font-size: medium; background: white;">framework of exchangeable arrays subject to bond percolation, we prove</span> <span style=" font-size: medium; background: white;">consistency of network histogram estimation under general conditions,</span> <span style=" font-size: medium; background: white;">giving rates of convergence which include the important practical setting</span> <span style=" font-size: medium; background: white;">of sparse networks</span><span style=" text-align: start; word-spacing: 0px; float: none; -webkit-text-stroke-width: 0px; orphans: auto; widows: auto; font-size: medium;">.</span></span></p>Nlorieannbzuniga1396271578747c1b321f798405410VgnVCM100000c2b1d38d____once11112newnewPatrick Wolfe, Ph.D., Professor, Department of Statistical Science, University College Londonhttp://www.ucl.ac.uk/