We introduce the speculate-correct method to derive error bounds for local classifiers. Using it, we show that k nearest neighbor classifiers, in spite of their famously fractured decision boundaries, have exponential error bounds with O(sqrt((k + ln n) / n)) error bound range for n in-sample examples.
Cite
@article{arxiv.1410.2500,
title = {Speculate-Correct Error Bounds for k-Nearest Neighbor Classifiers},
author = {Eric Bax and Lingjie Weng and Xu Tian},
journal= {arXiv preprint arXiv:1410.2500},
year = {2017}
}