Non-Asymptotic Uniform Rates of Consistency for k-NN Regression

Abstract We derive high-probability finite-sample uniform rates of consistency for k-NN regression that are optimal up to logarithmic factors under mild assumptions. We moreover show that k-NN regression adapts to an unknown lower intrinsic dimension automatically in the sup-norm. We then apply the k-NN regression rates to establish new results about estimating the level sets and global maxima of a function from noisy observations.