Optimal weighted nearest neighbour classifiers
نویسندگان
چکیده
منابع مشابه
Optimal weighted nearest neighbour classifiers
We derive an asymptotic expansion for the excess risk (regret) of a weighted nearest-neighbour classifier. This allows us to find the asymptotically optimal vector of nonnegative weights, which has a rather simple form. We show that the ratio of the regret of this classifier to that of an unweighted k-nearest neighbour classifier depends asymptotically only on the dimension d of the feature vec...
متن کاملTo “ Optimal Weighted Nearest Neighbour Classifiers ”
Completion of the proof of Theorem 1. Step 6: To show (6.5), which gives the Radon–Nikodym derivative of the restriction of the distribution of X(i) − x to a small ball about the origin Recall that Bδ(u) = {y ∈ Rd : ‖y − u‖ ≤ δ}, and that νd denotes ddimensional Lebesgue measure. For a Borel subset A of Rd, let N(A) = ∑n i=1 1{Xi∈A}. It follows from the hypothesis (A.2) that for x ∈ S n with n ...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2012
ISSN: 0090-5364
DOI: 10.1214/12-aos1049