Differentially Private Numerical Vector Analyses in the Local and Shuffle Model

doi:10.1109/TDSC.2023.3340178

Differentially Private Numerical Vector Analyses in the Local and Shuffle Model

2025-01-01

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DOI：10.1109/TDSC.2023.3340178

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Numerical vector aggregation plays a crucial role in privacy-sensitive applications, such as distributed gradient estimation in federated learning and statistical analysis of key-value data. In the context of local differential privacy, this study provides a tight minimax error bound of O(ds/n epsilon(2)), where d represents the dimension of the numerical vector and s denotes the number of non-zero entries. By converting the conditional/unconditional numerical mean estimation problem into a frequency estimation problem, we develop an optimal and efficient mechanism called Collision. In contrast, existing methods exhibit sub-optimal error rates of O(d(2)/n epsilon(2)) or O(ds(2)/n epsilon(2)). Specifically, for unconditional mean estimation, we leverage the negative correlation between two frequencies in each dimension and propose the CoCo mechanism, which further reduces estimation errors for mean values compared to Collision. Moreover, to surpass the error barrier in local privacy, we examine privacy amplification in the shuffle model for the proposed mechanisms and derive precisely tight amplification bounds. Our experiments validate and compare our mechanisms with existing approaches, demonstrating significant error reductions for frequency estimation and mean estimation on numerical vectors.

Keywords:

Estimation

Privacy

Numerical models

Differential privacy

Frequency estimation

Computational modeling

Data models

Data aggregation

local differential privacy

mean estimation

minimax error bound

shuffle model

Differentially Private Numerical Vector Analyses in the Local and Shuffle Model

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