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Location-Based Services (LBS) are becoming more prevalent. While there are many benefits, there are also real privacy risks. People are unwilling to give up the benefits -but can we reduce privacy risks without giving up on LBS entirely? This paper explores the possibility of introducing uncertainty into location information when using an LBS, so as to reduce privacy risk while maintaining good quality of service. This paper also explores the current uses of uncertainty information in a selection of mobile applications.

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.

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