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SUMMARY:Local nearest neighbour classification with applications to semi-s
 upervised learning - Thomas Berrett (University of Cambridge)
DTSTART:20170531T150000Z
DTEND:20170531T160000Z
UID:TALK72590@talks.cam.ac.uk
CONTACT:Nicolai Baldin
DESCRIPTION:In this talk I will present a new asymptotic expansion for the
  global excess risk of a local k-nearest neighbour classifier\, where the 
 choice of k may depend upon the test point. This expansion elucidates cond
 itions under which the dominant contribution to the excess risk comes from
  the locus of points at which each class label is equally likely to occur.
  Moreover\, I will present results which show that\, provided the d-dimens
 ional marginal distribution of the features has a finite ρth moment for s
 ome ρ>4 (as well as other regularity conditions)\, a local choice of k ca
 n yield a rate of convergence of the excess risk of O(n^(-4/(d+4)))\, wher
 e n is the sample size\, whereas for the standard k-nearest neighbour clas
 sifier\, our theory would require d≥5 and ρ>4d/(d−4) finite moments t
 o achieve this rate. Motivated by these results\, I will introduce a new k
 -nearest neighbour classifier for semi-supervised learning problems\, wher
 e the unlabelled data are used to obtain an estimate of the marginal featu
 re density\, and fewer neighbours are used for classification when this de
 nsity estimate is small.
LOCATION:MR14\, Centre for Mathematical Sciences
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