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CATEGORIES:ML@CL Seminar Series
SUMMARY:Maximum entropy\, uniform measure - Emily Roff\, S
chool of Mathematics\, Univeristy of Edinburgh
DTSTART;TZID=Europe/London:20201113T131500
DTEND;TZID=Europe/London:20201113T140000
UID:TALK151840AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/151840
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 entropies\, each
assigning a real number to any probability measur
e on a compact metric space (or\, more generally\,
a compact Hausdorff space with a notion of simila
rity between points). These entropies generalise t
he Shannon and Rényi entropies of information theo
ry.\nWe prove that on any space X\, there is a sin
gle probability measure maximising all these entro
pies simultaneously. Moreover\, all the entropies
have the same maximum value: the maximum entropy o
f X. As X is scaled up\, the maximum entropy grows
\; its asymptotics determine geometric information
about X\, including the volume and dimension. We
also study the large-scale limit of the maximising
measure itself\, arguing that it should be regard
ed as the canonical or uniform measure on X. \n\n\
n*Keywords:* Maximum Entropy\, Enriched Categories
\, Size and Magnitude\, metric spaces.\n\n*About t
he Speaker:*\n\nEmily Roff is a PhD student at the
University of Edinburgh\, where she is a member o
f the Geometry and Topology group in the Hodge Ins
titute\, working with Tom Leinster. Emily's resear
ch has to do with numerical and homological invari
ants of metric spaces that derive from an interpre
tation of a metric space as a type of enriched cat
egory. More generally\, she is interested in enric
hed category theory and its applications within an
d beyond pure mathematics. Prior to Edinburgh Emil
y 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 foc
using on early career researchers in topics releva
nt to machine learning and statistics.
LOCATION: https://dtudk.zoom.us/j/69745050502?pwd=RzV3UWtMW
jgzMko4cFhSNFM3T1FEdz09
CONTACT:Francisco Vargas
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