37,814 research outputs found
Discrete Distribution Estimation under Local Privacy
Abstract The collection and analysis of user data drives improvements in the app and web ecosystems, but comes with risks to privacy. This paper examines discrete distribution estimation under local privacy, a setting wherein service providers can learn the distribution of a categorical statistic of interest without collecting the underlying data. We present new mechanisms, including hashed k-ary Randomized Response (k-RR), that empirically meet or exceed the utility of existing mechanisms at all privacy levels. New theoretical results demonstrate the order-optimality of k-RR and the existing RAPPOR mechanism at different privacy regimes
Discrete Distribution Estimation under User-level Local Differential Privacy
We study discrete distribution estimation under user-level local differential
privacy (LDP). In user-level -LDP, each user has samples
and the privacy of all samples must be preserved simultaneously. We resolve
the following dilemma: While on the one hand having more samples per user
should provide more information about the underlying distribution, on the other
hand, guaranteeing the privacy of all samples should make the estimation
task more difficult. We obtain tight bounds for this problem under almost all
parameter regimes. Perhaps surprisingly, we show that in suitable parameter
regimes, having samples per user is equivalent to having times more
users, each with only one sample. Our results demonstrate interesting phase
transitions for and the privacy parameter in the estimation
risk. Finally, connecting with recent results on shuffled DP, we show that
combined with random shuffling, our algorithm leads to optimal error guarantees
(up to logarithmic factors) under the central model of user-level DP in certain
parameter regimes. We provide several simulations to verify our theoretical
findings.Comment: 26 pages, 4 figure
- …