Optimal differential privacy mechanisms under Hamming distortion for structured source classes
Kousha Kalantari, Lalitha Sankar, Anand D. Sarwate · 2016
We examine a tradeoff between privacy and utility in terms of local differential privacy (L-DP) and Hamming distortion for certain classes of finite-alphabet sources under Hamming distortion. We define two classes: permutation-invariant, and ordered statistics (whose probability mass functions are monotonic). We obtain the optimal L-DP mechanism for permutation-invariant sources and derive upper and lower bounds on the achievable local differential privacy for ordered statistics for a range of target distortion values.