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SUMMARY:Laszlo Csirmaz (Budapest)
DTSTART:20260211T160000Z
DTEND:20260211T171500Z
DTSTAMP:20260423T021406Z
UID:AAIT/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AAIT/48/">In
 formation Inequalities for Five Random Variables.</a>\nby Laszlo Csirmaz (
 Budapest) as part of Seminar on Algorithmic Aspects of Information Theory\
 n\n\nAbstract\nSplit the base set N into the disjoint union YXZ\, and let 
 Y1\,...\,Yn be copies of Y\, and Z1\,...\,Zm be copies of Z. For any proba
 bility distribution on YXZ there is another probability distribution on (Y
 1 ... Yn X Z1 ... Zm) such that the marginals on XYi and XY are the same\;
  the marginals on XZj and XZ are the same\; moreover the variable sets {Yi
 \,Zj} are completely conditionally independent over X.\n\nApplying this pr
 operty for Y={cd}\, X={ab}\, and Z={z}\, all consequences are computed for
  n<10. Based on the results\, two infinite families of five-variable non-S
 hannon inequalities are defined and proved to be consequences of the above
  property. We investigate the “extremal” inequalities among them\, the
 ir asymptotic behavior\, and how they delimit the five-variable entropy re
 gion. At the end we discuss how they relate to Matus’ inequalities.\n
LOCATION:https://researchseminars.org/talk/AAIT/48/
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