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SUMMARY:A local weak limit approach to the study of graphical data - Prof.
  Venkat Anantharam\, University of California\, Berkeley
DTSTART:20190521T140000Z
DTEND:20190521T150000Z
UID:TALK123655@talks.cam.ac.uk
CONTACT:Prof. Ramji Venkataramanan
DESCRIPTION:By *graphical data*\, we mean data indexed by the vertices and
  edges of a sparse graph rather than by linearly ordered time. Just as a s
 tochastic process is a stochastic model for a time series got by picking a
  time index at random and viewing how the time series looks from that time
 \nindex\, in the local weak limit theory one studies graphical data by pic
 king a node  of the graph at random and seeing how the data looks from the
  point of view of that node. What results is a so-called sofic distributio
 n on  rooted marked graphs.\n\nBordenave and Caputo (2014) defined a notio
 n of entropy for probability distributions on rooted graphs with finite ex
 pected degree at the root. \nWe call this BC entropy. We develop the paral
 lel result for probability distributions on marked rooted graphs.  Our gra
 phs have vertex marks drawn from a finite set and directed edge marks\, on
 e towards each vertex\, drawn from a finite set.\n\nWe develop the details
  of our generalization of BC entropy to the case of rooted marked graphs. 
 We then illustrate the value of this viewpoint by proving a universal loss
 less data compression theorem analogous to the basic universal lossless da
 ta compression theorem for time series.\nWe also prove\, for graphical dat
 a\, an analog of the Slepian-Wolf theorem of distributed compression  for 
 Erdos-Renyi and configuration model ensembles.\n\nThis is joint work with 
 Payam Delgosha.\n
LOCATION:LT6\, Baker Building\, CUED
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