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SUMMARY:Maximum entropy\, uniform measure - Emily Roff\, School of Mathema
 tics\, Univeristy of Edinburgh
DTSTART:20201113T131500Z
DTEND:20201113T140000Z
UID:TALK151840@talks.cam.ac.uk
CONTACT:Francisco Vargas
DESCRIPTION:*Paper:*\n\nTalk is based on "this":https://arxiv.org/pdf/1908
 .11184.pdf paper.\n\n*Abstract:*\n\nWe define a one-parameter family of en
 tropies\, each assigning a real number to any probability measure on a com
 pact metric space (or\, more generally\, a compact Hausdorff space with a 
 notion of similarity between points). These entropies generalise the Shann
 on and Rényi entropies of information theory.\nWe prove that on any space
  X\, there is a single probability measure maximising all these entropies 
 simultaneously. Moreover\, all the entropies have the same maximum value: 
 the maximum entropy of X. As X is scaled up\, the maximum entropy grows\; 
 its asymptotics determine geometric information about X\, including the vo
 lume and dimension. We also study the large-scale limit of the maximising 
 measure itself\, arguing that it should be regarded as the canonical or un
 iform measure on X. \n\n\n*Keywords:* Maximum Entropy\, Enriched Categorie
 s\, Size and Magnitude\, metric spaces.\n\n*About the Speaker:*\n\nEmily R
 off is a PhD student at the University of Edinburgh\, where she is a membe
 r of the Geometry and Topology group in the Hodge Institute\, working with
  Tom Leinster. Emily's research has to do with numerical and homological i
 nvariants of metric spaces that derive from an interpretation of a metric 
 space as a type of enriched category. More generally\, she is interested i
 n enriched category theory and its applications within and beyond pure mat
 hematics. Prior to Edinburgh Emily completed part III of the mathematical 
 Tripos at Cambridge.\n\n*Website:* https://www.maths.ed.ac.uk/~emilyroff/\
 n\nPart of ML@CL Seminar Series focusing on early career researchers in to
 pics relevant to machine learning and statistics.
LOCATION: https://dtudk.zoom.us/j/69745050502?pwd=RzV3UWtMWjgzMko4cFhSNFM3
 T1FEdz09
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