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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Sparse and modular networks using exchangeable ran
dom measures - Francois Caron (University of Oxfor
d)
DTSTART;TZID=Europe/London:20160711T153000
DTEND;TZID=Europe/London:20160711T160000
UID:TALK66702AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/66702
DESCRIPTION:Statistical network modeling has focused on repres
enting the graph as a discrete struc
ture\, namely the adjacency matrix\,
and considering the exchangeability of this array
. In such cases\, it is well known t
hat the graph is necessarily either
dense (the number of edges scales qu
adratically with the number of nodes) or trivially
empty.

Here\, we
instead consider representing the graph as a
measure on the plane. For the associated
definition of exchangeability\, we
rely on the Kallenberg representation
theorem (Kallenberg\, 1990). For certain choices
of such exchangeable random measure
s underlying the graph construction\
, the network process is sparse with power-law
degree distribution\, and can accommoda
te an overlapping block-structure. <
br> A Markov chain Monte Carlo algor
ithm is derived for efficient explor
ation of the posterior distribution and allows to
recover the structure of a range of
networks ranging from dense to sparse
based on our flexible formulation.

Joint work with Emily Fox
and Adrien Todeschini

http://arxiv.org/abs/1401.1137

http://arxiv
.org/pdf/1602.02114

LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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