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SUMMARY:Efficient multivariate entropy estimation via k-nearest neighbour 
 distances - Tom Berrett\, DPMMS/Statslab
DTSTART:20170427T134000Z
DTEND:20170427T142000Z
UID:TALK72154@talks.cam.ac.uk
CONTACT:Jack Smith
DESCRIPTION:Many widely-used statistical procedures\, including methods fo
 r goodness-of-fit tests\, feature selection and changepoint analysis\, rel
 y critically on the estimation of the entropy of a distribution. I will in
 itially present new results on a commonly used generalisation of the estim
 ator originally proposed by Kozachenko and Leonenko (1987)\, which is base
 d on the k-nearest neighbour distances of a sample of independent and iden
 tically distributed random vectors. These results show that\, in up to 3 d
 imensions and under regularity conditions\, the estimator is efficient for
  certain choices of k\, in the sense of achieving the local asymptotic min
 imax lower bound. However\, they also show that in higher dimensions a non
 -trivial bias precludes its efficiency regardless of the choice of k. This
  motivates us to consider a new entropy estimator\, formed as a weighted a
 verage of Kozachenko-Leonenko estimators for different values of k. A care
 ful choice of weights enables us to reduce the bias of the first estimator
  and thus obtain an efficient estimator in arbitrary dimensions\, given su
 fficient smoothness. Our results provided theoretical insight and have imp
 ortant methodological implications.
LOCATION:MR3\, CMS
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