  Local differential privacy (LDP) has received much interest recently. In
existing protocols with LDP guarantees, a user encodes and perturbs his data
locally before sharing it to the aggregator. In common practice, however, users
would prefer not to answer all the questions due to different
privacy-preserving preferences for different questions, which leads to data
missing or the loss of data quality. In this paper, we demonstrate a new
approach for addressing the challenges of data perturbation with consideration
of users' privacy preferences. Specifically, we first propose BiSample: a
bidirectional sampling technique value perturbation in the framework of LDP.
Then we combine the BiSample mechanism with users' privacy preferences for
missing data perturbation. Theoretical analysis and experiments on a set of
datasets confirm the effectiveness of the proposed mechanisms.
