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CATEGORIES:Statistics
SUMMARY:Histograms\, Graph Limits\, and the Asymptotic Beh
avior of Large Networks - Sofia Olhede\, Universit
y College London
DTSTART;TZID=Europe/London:20140516T160000
DTEND;TZID=Europe/London:20140516T170000
UID:TALK52255AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/52255
DESCRIPTION:Networks are fast becoming part of the modern stat
istical landscape. Yet we lack a full understandin
g of their large-sample properties in all but the
simplest settings. This is hindering the developme
nt of models and estimation methods that admit the
oretical performance guarantees. The asymptotic be
havior of large networks can be exploited for nonp
arametric statistical inference\, using recent dev
elopments from the theory of graph limits\, and th
e corresponding analog of de Finetti's theorem.\n\
n\nA network histogram is obtained by fitting a st
ochastic blockmodel to a single observation of a n
etwork dataset. Blocks of edges play the role of h
istogram bins\, and community sizes that of histog
ram bandwidths or bin sizes. Just as standard hist
ograms allow for varying bandwidths\, different bl
ockmodel estimates can all be considered valid rep
resentations of an underlying probability model\,
subject to bandwidth constraints. We show that und
er these constraints\, the mean integrated square
error of the network histogram tends to zero as th
e network grows large\, and we provide methods for
optimal bandwidth selection-thus making the block
model a universal representation. With this insigh
t\, we discuss the interpretation of network commu
nities in light of the fact that many different co
mmunity assignments can all give an equally valid
representation of the network.\n\n\nTo demonstrate
the fidelity-versus-interpretability tradeoff inh
erent in considering different numbers and sizes o
f communities\, we show an example of detecting an
d describing new network community microstructure
in political weblog data. \n\n\nThis is joint work
with Patrick Wolfe - UCLâ€‹\n
LOCATION:MR12\, Centre for Mathematical Sciences\, Wilberf
orce Road\, Cambridge
CONTACT:
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