  When applying outlier detection in settings where data is sensitive,
mechanisms which guarantee the privacy of the underlying data are needed. The
$k$-nearest neighbors ($k$-NN) algorithm is a simple and one of the most
effective methods for outlier detection. So far, there have been no attempts
made to develop a differentially private ($\epsilon$-DP) approach for $k$-NN
based outlier detection. Existing approaches often relax the notion of
$\epsilon$-DP and employ other methods than $k$-NN. We propose a method for
$k$-NN based outlier detection by separating the procedure into a fitting step
on reference inlier data and then apply the outlier classifier to new data. We
achieve $\epsilon$-DP for both the fitting algorithm and the outlier classifier
with respect to the reference data by partitioning the dataset into a uniform
grid, which yields low global sensitivity. Our approach yields nearly optimal
performance on real-world data with varying dimensions when compared to the
non-private versions of $k$-NN.
