LOCAL NEAREST NEIGHBOUR CLASSIFICATION WITH APPLICATIONS TO SEMI-SUPERVISED LEARNING
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Abstract
We derive a new asymptotic expansion for the global excess risk of a
local-
4d/(d-4)$ finite moments to achieve this rate. These results motivate a new
-nearest neighbour classifier for semi-supervised learning problems, where the unlabelled data are used to obtain an estimate of the marginal feature density, and fewer neighbours are used for classification when this density estimate is small. Our worst-case rates are complemented by a minimax lower bound, which reveals that the local, semi-supervised -nearest neighbour classifier attains the minimax optimal rate over our classes for the excess risk, up to a subpolynomial factor in . These theoretical improvements over the standard -nearest neighbour classifier are also illustrated through a simulation study.
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Leverhulme Trust (PLP-2014-353)
Engineering and Physical Sciences Research Council (EP/N031938/1)
Engineering and Physical Sciences Research Council (EP/P031447/1)