Differentially Private Analysis of Outliers

This paper presents an investigation of differentially private analysis of distance-based outliers. Outlier detection aims to identify instances that are apparently distant from other instances. Meanwhile, the objective of differential privacy is to conceal the presence (or absence) of any particular instance. Outlier detection and privacy protection are therefore intrinsically conflicting tasks. In this paper, we present differentially private queries for counting outliers that appear in a given subspace, instead of reporting the outliers detected. Our analysis of the global sensitivity of outlier counts reveals that regular global sensitivity-based methods can make the outputs too noisy, particularly when the dimensionality of the given subspace is high. Noting that the counts of outliers are typically expected to be small compared to the number of data, we introduce a mechanism based on the smooth upper bound of the local sensitivity. This study is the first trial to ensure differential privacy for distance-based outlier analysis. The experimentally obtained results show that our method achieves better utility than global sensitivity-based methods do.