Differentially Private k-Nearest Neighbor Missing Data Imputation

Using techniques employing smooth sensitivity, we develop a method for k-nearest neighbor missing data imputation with differential privacy. This requires bounding the number of data incomplete tuples that can have their data complete "donor" changed by making a single addition or deletion to the dataset. The multiplicity of a single individual's impact on an imputed dataset necessarily means our mechanisms require the addition of more noise than mechanisms that ignore missing data, but we show empirically that this is significantly outweighed by the bias reduction from imputing missing data.