Locally Differentially Private Sparse Vector Aggregation

12/07/2021
by   Mingxun Zhou, et al.
0

Vector mean estimation is a central primitive in federated analytics. In vector mean estimation, each user i ∈ [n] holds a real-valued vector v_i∈ [-1, 1]^d, and a server wants to estimate the mean of all n vectors. Not only so, we would like to protect each individual user's privacy. In this paper, we consider the k-sparse version of the vector mean estimation problem, that is, suppose that each user's vector has at most k non-zero coordinates in its d-dimensional vector, and moreover, k ≪ d. In practice, since the universe size d can be very large (e.g., the space of all possible URLs), we would like the per-user communication to be succinct, i.e., independent of or (poly-)logarithmic in the universe size. In this paper, we are the first to show matching upper- and lower-bounds for the k-sparse vector mean estimation problem under local differential privacy. Specifically, we construct new mechanisms that achieve asymptotically optimal error as well as succinct communication, either under user-level-LDP or event-level-LDP. We implement our algorithms and evaluate them on synthetic as well as real-world datasets. Our experiments show that we can often achieve one or two orders of magnitude reduction in error in comparison with prior works under typical choices of parameters, while incurring insignificant communication cost.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/01/2019

Lower Bounds for Locally Private Estimation via Communication Complexity

We develop lower bounds for estimation under local privacy constraints--...
research
04/10/2023

Differentially Private Numerical Vector Analyses in the Local and Shuffle Model

Numerical vector aggregation plays a crucial role in privacy-sensitive a...
research
06/07/2023

Fast Optimal Locally Private Mean Estimation via Random Projections

We study the problem of locally private mean estimation of high-dimensio...
research
10/18/2018

Locally Private Mean Estimation: Z-test and Tight Confidence Intervals

This work provides tight upper- and lower-bounds for the problem of mean...
research
02/18/2023

Differential Aggregation against General Colluding Attackers

Local Differential Privacy (LDP) is now widely adopted in large-scale sy...
research
02/21/2020

Distributed Mean Estimation with Optimal Error Bounds

Motivated by applications to distributed optimization and machine learni...
research
10/14/2021

Leveraging Spatial and Temporal Correlations in Sparsified Mean Estimation

We study the problem of estimating at a central server the mean of a set...

Please sign up or login with your details

Forgot password? Click here to reset