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CATEGORIES:Statistics
SUMMARY:Root and community inference on Markovian models o
f networks - Min Xu (Rutgers University)
DTSTART;TZID=Europe/London:20221021T140000
DTEND;TZID=Europe/London:20221021T150000
UID:TALK182720AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/182720
DESCRIPTION:Preferential attachment (PA) is a popular way of m
odeling random networks in which the network start
s as a single node which we call the root node\, a
nd at every new time step\, a new node and new edg
es are added to the network\; this dynamic capture
s the growth/recruitment process that underlies ma
ny real-world networks.\n\nGiven only a single sna
pshot of the final network G\, we study the proble
m of constructing confidence sets for the early hi
story\, in particular the root node\, of the unobs
erved growth process\; the root node can be patien
t zero in a disease infection network or the sourc
e of fake news in a social media network.\n\nWe co
nsider random network generated by adding noisy ed
ges to a PA tree and derive an inference algorithm
based on Gibbs sampling that scales to networks w
ith millions of nodes. We provide theoretical anal
ysis showing that the expected size of the confide
nce set is small so long as the noise level is not
too large. We also propose variations of the mode
l in which multiple growth processes occur simulta
neously from multiple root nodes\, reflecting the
formation of multiple communities\, and we use the
se models to provide a new approach to community d
etection.
LOCATION:MR12\, Centre for Mathematical Sciences
CONTACT:Qingyuan Zhao
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