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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Compressed Empirical Measures - Steffen Grunewal
der (Lancaster University - Mathematics and Statis
tic Dept.)
DTSTART;TZID=Europe/London:20180329T110000
DTEND;TZID=Europe/London:20180329T120000
UID:TALK103237AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/103237
DESCRIPTION:I will present results on compressed representatio
ns of expectation operators with a particular emph
asis on expectations with respect to empirical mea
sures. Such expectations are a cornerstone of non-
parametric statistics and compressed representatio
ns are of great value when dealing with large samp
le sizes and computationally expensive methods. I
will focus on a conditional gradient like algorith
m to generate such representations in infinite dim
ensional function spaces. In particular\, I will d
iscuss extensions of classical convergence results
to uniformly smooth Banach spaces (think Lp\, 1 &
lt\; p <\; 1\, or various scales of Besov and So
bolev spaces)\; a counter example to fast rates of
convergence in norm when compact sets are used fo
r approximations\; workarounds based on slicing co
mpact sets in suitable ways and a result about fas
t convergence when the norm convergence is replace
d with a weaker form of convergence\; results abou
t the location of the representer of a probability
measure inside the approximation set using smooth
ness assumptions on the point-evaluators\; and an
application of these results to empirical processe
s.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:INI IT
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