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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:TALK103234AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/103234
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 <
p < 1\, or various scales of Besov and Sobolev sp
aces)\; a counter example to fast rates of converg
ence in norm when compact sets are used for approx
imations\; workarounds based on slicing compact se
ts in suitable ways and a result about fast conver
gence when the norm convergence is replaced with a
weaker form of convergence\; results about the lo
cation of the representer of a probability measure
inside the approximation set using smoothness ass
umptions on the point-evaluators\; and an applicat
ion of these results to empirical processes.

LOCATION:Seminar Room 2\, Newton Institute
CONTACT:info@newton.ac.uk
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