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CATEGORIES:Cambridge Analysts' Knowledge Exchange
SUMMARY:Local nearest neighbour classification with applic
ations to semi-supervised learning - Thomas Berret
t (University of Cambridge)
DTSTART;TZID=Europe/London:20170531T160000
DTEND;TZID=Europe/London:20170531T170000
UID:TALK72590AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/72590
DESCRIPTION:In this talk I will present a new asymptotic expan
sion for the global excess risk of a local k-neare
st neighbour classifier\, where the choice of k ma
y depend upon the test point. This expansion eluci
dates conditions under which the dominant contribu
tion to the excess risk comes from the locus of po
ints at which each class label is equally likely t
o occur. Moreover\, I will present results which s
how that\, provided the d-dimensional marginal dis
tribution of the features has a finite ρth moment
for some ρ>4 (as well as other regularity conditio
ns)\, a local choice of k can yield a rate of conv
ergence of the excess risk of O(n^(-4/(d+4)))\, wh
ere n is the sample size\, whereas for the standar
d k-nearest neighbour classifier\, our theory woul
d require d≥5 and ρ>4d/(d−4) finite moments to ach
ieve this rate. Motivated by these results\, I wil
l introduce a new k-nearest neighbour classifier f
or semi-supervised learning problems\, where the u
nlabelled data are used to obtain an estimate of t
he marginal feature density\, and fewer neighbours
are used for classification when this density est
imate is small.
LOCATION:MR14\, Centre for Mathematical Sciences
CONTACT:Nicolai Baldin
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