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Non-Asymptotic Uniform Rates of Consistency for k-NN Regression
We derive high-probability finite-sample uniform rates of consistency for
-NN regression that are optimal up to logarithmic factors under mild
assumptions. We moreover show that -NN regression adapts to an unknown lower
intrinsic dimension automatically. We then apply the -NN regression rates to
establish new results about estimating the level sets and global maxima of a
function from noisy observations.Comment: In Proceedings of 33rd AAAI Conference on Artificial Intelligence
(AAAI 2019
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