1 research outputs found
Locally Differentially Private Minimum Finding
We investigate a problem of finding the minimum, in which each user has a
real value and we want to estimate the minimum of these values under the local
differential privacy constraint. We reveal that this problem is fundamentally
difficult, and we cannot construct a mechanism that is consistent in the worst
case. Instead of considering the worst case, we aim to construct a private
mechanism whose error rate is adaptive to the easiness of estimation of the
minimum. As a measure of easiness, we introduce a parameter that
characterizes the fatness of the minimum-side tail of the user data
distribution. As a result, we reveal that the mechanism can achieve
error without knowledge of and
the error rate is near-optimal in the sense that any mechanism incurs
error. Furthermore, we demonstrate that
our mechanism outperforms a naive mechanism by empirical evaluations on
synthetic datasets. Also, we conducted experiments on the MovieLens dataset and
a purchase history dataset and demonstrate that our algorithm achieves
error adaptively to