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SUMMARY:Root and community inference on Markovian models of networks - Min
  Xu (Rutgers University)
DTSTART:20221021T130000Z
DTEND:20221021T140000Z
UID:TALK182720@talks.cam.ac.uk
CONTACT:Qingyuan Zhao
DESCRIPTION:Preferential attachment (PA) is a popular way of modeling rand
 om networks in which the network starts as a single node which we call the
  root node\, and at every new time step\, a new node and new edges are add
 ed to the network\; this dynamic captures the growth/recruitment process t
 hat underlies many real-world networks.\n\nGiven only a single snapshot of
  the final network G\, we study the problem of constructing confidence set
 s for the early history\, in particular the root node\, of the unobserved 
 growth process\; the root node can be patient zero in a disease infection 
 network or the source of fake news in a social media network.\n\nWe consid
 er random network generated by adding noisy edges to a PA tree and derive 
 an inference algorithm based on Gibbs sampling that scales to networks wit
 h millions of nodes. We provide theoretical analysis showing that the expe
 cted size of the confidence set is small so long as the noise level is not
  too large. We also propose variations of the model in which multiple grow
 th processes occur simultaneously from multiple root nodes\, reflecting th
 e formation of multiple communities\, and we use these models to provide a
  new approach to community detection.
LOCATION:MR12\, Centre for Mathematical Sciences
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