Validation of k-Nearest Neighbor Classifiers Using Inclusion and Exclusion
This paper presents a series of PAC exponential error bounds for $k$-nearest neighbors classifiers, with O($n^{-\frac{r}{2r+1}}\sqrt{k \ln n}$) error bound range for each integer $r>0$, where $n$ is the number of in-sample examples. This shows that $k$-nn classifiers, in spite of their famously fractured decision boundaries, come close to having Gaussian-style exponential error bounds with O($n^{-\frac{1}{2}}$) bound ranges.