{"ID":2856182,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.11116","arxiv_id":"2510.11116","title":"N-output Mechanism: Estimating Statistical Information from Numerical Data under Local Differential Privacy","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2510.11116","url_pdf":"https://arxiv.org/pdf/2510.11116v1","authors":"[\"Incheol Baek\",\"Yon Dohn Chung\"]","published":"2025-10-13T08:06:59Z","proceeding":"cs.CR","tasks":"[\"cs.CR\"]","methods":"[]","has_code":false}