Eprints of Rényi Institute

Structure of the entropy region

Csirmaz, László (2014) Structure of the entropy region. In: Unemat3, July 28-31, 2014, Universidad Nacional de Colombia, Bogota, Colombia.

PDF (Lecture I)
PDF (Lecture II)
PDF (Lecture III)


The entropies of all non-empty subsets of several jointly distributed random variables form the entropy vector; the entropy region is the collection of all entropy vectors. In this series of lectures we present some very recent results on the structure of the entropy region. Lecture I investigates the two and three variable case, defines the "ringing bells" distribution, defines linear and group-based distributions. Lecture II introduces polymatroids, proves that the closure of the entropy region is a closed convex full-dimensional cone where every internal point is entropic. It concludes by proving the correctness of the four known methods which can obtain new linear entropy inequalities. Lecture III gives a self-contained proof of F. Matus stating that the entropy region is not polyhedral. The lecture concludes with some ideas on how to show that the entropy region is not semi-algebraic.

Item Type:Conference or Workshop Item (Lecture)
Keywords and phrases:entropy region; polymatroid; Shannon entropy; polyhedral cone; entropy inequality; semi-algebraic set
Subjects:52B11 $n$-dimensional polytopes
05B35 Matroids, geometric lattices
94A17 Measures of information, entropy
Divisions:Research Groups > Theoretical cryptography
Last Modified:01 Sep 2014 14:40

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