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CATEGORIES:Signal Processing and Communications Lab Seminars
SUMMARY:A local weak limit approach to the study of graphi
cal data - Prof. Venkat Anantharam\, University of
California\, Berkeley
DTSTART;TZID=Europe/London:20190521T150000
DTEND;TZID=Europe/London:20190521T160000
UID:TALK123655AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/123655
DESCRIPTION:By *graphical data*\, we mean data indexed by the
vertices and edges of a sparse graph rather than b
y linearly ordered time. Just as a stochastic proc
ess is a stochastic model for a time series got by
picking a time index at random and viewing how th
e time series looks from that time\nindex\, in the
local weak limit theory one studies graphical dat
a by picking a node of the graph at random and se
eing how the data looks from the point of view of
that node. What results is a so-called sofic distr
ibution on rooted marked graphs.\n\nBordenave and
Caputo (2014) defined a notion of entropy for pro
bability distributions on rooted graphs with finit
e expected degree at the root. \nWe call this BC e
ntropy. We develop the parallel result for probabi
lity distributions on marked rooted graphs. Our g
raphs have vertex marks drawn from a finite set an
d directed edge marks\, one towards each vertex\,
drawn from a finite set.\n\nWe develop the details
of our generalization of BC entropy to the case o
f rooted marked graphs. We then illustrate the val
ue of this viewpoint by proving a universal lossle
ss data compression theorem analogous to the basic
universal lossless data compression theorem for t
ime series.\nWe also prove\, for graphical data\,
an analog of the Slepian-Wolf theorem of distribut
ed compression for Erdos-Renyi and configuration
model ensembles.\n\nThis is joint work with Payam
Delgosha.\n
LOCATION:LT6\, Baker Building\, CUED
CONTACT:Prof. Ramji Venkataramanan
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