Distribution Privacy Under Function Recoverability

A user generates $n$ independent and identically distributed data random variables with a probability mass function that must be guarded from querier. The querier recover, prescribed accuracy, given of the each query responses upon eliciting them user. chooses devises to maximize distribution privacy as gauged by (Kullback-Leibler) divergence between former querier’s best estimate it based on responses. Considering an arbitrary function, basic achievable lower bound for is provided does not depend corresponds worst-case privacy. Worst-case equals logsum cardinalities inverse atoms under number summands decreasing recovers improving accuracy. Next, upper (converse) (achievability) bounds privacy, dependent , are developed. improves latter so suitable assumptions; both converge grows. converse achievability proofs identify explicit strategies