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CATEGORIES:DPMMS PhD student colloquium
SUMMARY:Efficient multivariate entropy estimation via k-ne
arest neighbour distances - Tom Berrett\, DPMMS/St
atslab
DTSTART;TZID=Europe/London:20170427T144000
DTEND;TZID=Europe/London:20170427T152000
UID:TALK72154AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/72154
DESCRIPTION:Many widely-used statistical procedures\, includin
g methods for goodness-of-fit tests\, feature sele
ction and changepoint analysis\, rely critically o
n the estimation of the entropy of a distribution.
I will initially present new results on a commonl
y used generalisation of the estimator originally
proposed by Kozachenko and Leonenko (1987)\, which
is based on the k-nearest neighbour distances of
a sample of independent and identically distribute
d random vectors. These results show that\, in up
to 3 dimensions and under regularity conditions\,
the estimator is efficient for certain choices of
k\, in the sense of achieving the local asymptotic
minimax lower bound. However\, they also show tha
t in higher dimensions a non-trivial bias preclude
s its efficiency regardless of the choice of k. Th
is motivates us to consider a new entropy estimato
r\, formed as a weighted average of Kozachenko-Leo
nenko estimators for different values of k. A care
ful choice of weights enables us to reduce the bia
s of the first estimator and thus obtain an effici
ent estimator in arbitrary dimensions\, given suff
icient smoothness. Our results provided theoretica
l insight and have important methodological implic
ations.
LOCATION:MR3\, CMS
CONTACT:Jack Smith
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