具有有效统计的差异私有直方图

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2025-01-03 DOI:10.1016/j.spl.2024.110354

Zilong Cao , Shisong Wu , Xuanang Li , Hai Zhang

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引用次数: 0

摘要

差分私有直方图（DP-Histograms）是数据发布和隐私保护工作不可或缺的一部分。然而，传统的dp直方图往往不能保留有效的统计信息和原始数据的基本特征。本文指出了方差无效是一般dp -直方图的固有缺点，并提出了一种新的算法——有效统计差分私有直方图（VSDPH）来克服这一问题。基于线性规划和有界Lipschitz距离的VSDPH在保留原始数据的有效统计量的同时有效地生成DP直方图。我们的理论分析表明，由VSDPH产生的直方图保持渐近有效方差，并基于1-Wasserstein距离建立了上界。通过实验，我们验证了VSDPH能够准确地保持原始数据的统计特征。这种功能使生成的直方图更接近原始图。

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Differentially private histogram with valid statistics

Differentially private histograms (DP-Histograms) are integral to data publication and privacy preservation efforts. However, conventional DP-Histograms often fail to preserve valid statistical information and the essential characteristics of the original data. This paper shows the invalidity of variance is the inherent shortcomings in general DP-Histograms, and introduces a novel algorithm called the Differentially Private Histogram with Valid Statistics (VSDPH) to overcome the problem. The VSDPH, grounded in linear programming and bounded Lipschitz distance, efficiently generates DP histograms while preserving the valid statistics of the original data. Our theoretical analysis demonstrates that histograms produced by VSDPH maintain asymptotically valid variance, and we establish an upper bound based on the 1-Wasserstein distance. Through experiments, we validate that VSDPH can accurately hold the statistical characteristics of the original data. This capability brings the resulting histograms closer to the originals.

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来源期刊

Statistics & Probability Letters 数学-统计学与概率论

CiteScore

1.60

自引率

0.00%

发文量

173

审稿时长

6 months

期刊介绍： Statistics & Probability Letters adopts a novel and highly innovative approach to the publication of research findings in statistics and probability. It features concise articles, rapid publication and broad coverage of the statistics and probability literature. Statistics & Probability Letters is a refereed journal. Articles will be limited to six journal pages (13 double-space typed pages) including references and figures. Apart from the six-page limitation, originality, quality and clarity will be the criteria for choosing the material to be published in Statistics & Probability Letters. Every attempt will be made to provide the first review of a submitted manuscript within three months of submission. The proliferation of literature and long publication delays have made it difficult for researchers and practitioners to keep up with new developments outside of, or even within, their specialization. The aim of Statistics & Probability Letters is to help to alleviate this problem. Concise communications (letters) allow readers to quickly and easily digest large amounts of material and to stay up-to-date with developments in all areas of statistics and probability. The mainstream of Letters will focus on new statistical methods, theoretical results, and innovative applications of statistics and probability to other scientific disciplines. Key results and central ideas must be presented in a clear and concise manner. These results may be part of a larger study that the author will submit at a later time as a full length paper to SPL or to another journal. Theory and methodology may be published with proofs omitted, or only sketched, but only if sufficient support material is provided so that the findings can be verified. Empirical and computational results that are of significant value will be published.