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SUMMARY:From Graphon to Graphex: Models and Estimators for Sparse Networks
  using Exchangeable Random Measures - Daniel Roy (University of Toronto)
DTSTART:20160726T133000Z
DTEND:20160726T140000Z
UID:TALK66853@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span><span>A major challenge for Bayesian network analysis is
  that we lack general nonparametric models of&nbsp\;sparse graphs. To meet
  this challenge\, we introduce and study&nbsp\;the general&nbsp\;class of 
 random graphs defined by the exchangeability of their <i>real-valued</i> v
 ertex labels\, an idea&nbsp\;inspired by a model due to&nbsp\;Caron and Fo
 x.&nbsp\;A straightforward adaptation of a&nbsp\;result by Kallenberg yiel
 ds a representation theorem: every such random&nbsp\;graph is characterize
 d by three (potentially random) components: a&nbsp\;nonnegative real I\, a
 n integrable function S : R+ to R+\, and a symmetric measurable function W
 :&nbsp\;R+^2 to [0\,1] that satisfies several weak integrability&nbsp\;con
 ditions. We call the triple (I\,S\,W) a <i>graphex</i>\, in analogy to&nbs
 p\;graphons\, which characterize the (dense) exchangeable graphs on the&nb
 sp\;</span>naturals. I will present some results about the structure and&n
 bsp\;consistent estimation of these random graphs.&nbsp\;This is joint wor
 k with Victor Veitch.</span>
LOCATION:Seminar Room 1\, Newton Institute
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