Saved in:
Bibliographic Details
Main Authors: Baek, Incheol, Chung, Yon Dohn
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2510.11116
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866917007649144832
author Baek, Incheol
Chung, Yon Dohn
author_facet Baek, Incheol
Chung, Yon Dohn
contents Local Differential Privacy (LDP) addresses significant privacy concerns in sensitive data collection. In this work, we focus on numerical data collection under LDP, targeting a significant gap in the literature: existing LDP mechanisms are optimized for either a very small ($|Ω| \in \{2, 3\}$) or infinite output spaces. However, no generalized method for constructing an optimal mechanism for an arbitrary output size $N$ exists. To fill this gap, we propose the \textbf{N-output mechanism}, a generalized framework that maps numerical data to one of $N$ discrete outputs. We formulate the mechanism's design as an optimization problem to minimize estimation variance for any given $N \geq 2$ and develop both numerical and analytical solutions. This results in a mechanism that is highly accurate and adaptive, as its design is determined by solving an optimization problem for any chosen $N$. Furthermore, we extend our framework and existing mechanisms to the task of distribution estimation. Empirical evaluations show that the N-output mechanism achieves state-of-the-art accuracy for mean, variance, and distribution estimation with small communication costs.
format Preprint
id arxiv_https___arxiv_org_abs_2510_11116
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle N-output Mechanism: Estimating Statistical Information from Numerical Data under Local Differential Privacy
Baek, Incheol
Chung, Yon Dohn
Cryptography and Security
Local Differential Privacy (LDP) addresses significant privacy concerns in sensitive data collection. In this work, we focus on numerical data collection under LDP, targeting a significant gap in the literature: existing LDP mechanisms are optimized for either a very small ($|Ω| \in \{2, 3\}$) or infinite output spaces. However, no generalized method for constructing an optimal mechanism for an arbitrary output size $N$ exists. To fill this gap, we propose the \textbf{N-output mechanism}, a generalized framework that maps numerical data to one of $N$ discrete outputs. We formulate the mechanism's design as an optimization problem to minimize estimation variance for any given $N \geq 2$ and develop both numerical and analytical solutions. This results in a mechanism that is highly accurate and adaptive, as its design is determined by solving an optimization problem for any chosen $N$. Furthermore, we extend our framework and existing mechanisms to the task of distribution estimation. Empirical evaluations show that the N-output mechanism achieves state-of-the-art accuracy for mean, variance, and distribution estimation with small communication costs.
title N-output Mechanism: Estimating Statistical Information from Numerical Data under Local Differential Privacy
topic Cryptography and Security
url https://arxiv.org/abs/2510.11116