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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Edge-exchangeable graphs\, sparsity\, and power la
ws - Diana Cai (University of Chicago)
DTSTART;TZID=Europe/London:20160727T120000
DTEND;TZID=Europe/London:20160727T123000
UID:TALK66859AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/66859
DESCRIPTION:Many popular network models rely on the assumption
of (vertex) exchangeability\, in which the distri
bution of the graph is invariant to relabelings of
the vertices. However\, the Aldous-Hoover theorem
guarantees that these graphs are dense or empty w
ith probability one\, whereas many real-world grap
hs are sparse. We present an alternative notion of
exchangeability for random graphs\, which we call
edge exchangeability\, in which the distribution
of a graph sequence is invariant to the order of t
he edges. We characterize the class of edge exchan
geable models with a paintbox construction\, and w
e demonstrate that edge-exchangeable models\, unli
ke models that are traditionally vertex exchangeab
le\, can exhibit sparsity and power laws. To do so
\, we outline a general framework for graph genera
tive models\; by contrast to the pioneering work o
f Caron and Fox (2014)\, models within our framewo
rk are stationary across steps of the graph sequen
ce. In particular\, our model grows the graph by i
nstantiating more latent atoms of a single random
measure as the dataset size increases\, rather tha
n adding new atoms to the measure.
Joint wo
rk with Trevor Campbell and Tamara Broderick.
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LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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