微分私有约束下尖刺协方差矩阵的上界

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Statistics & Probability Letters Pub Date : 2025-06-27 DOI:10.1016/j.spl.2025.110493

Chunguang Ren, Pei Zhang

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引用次数: 0

摘要

Cai, Xia, and Zha（2024）在schattenq范数下给出了高斯和亚高斯分布的尖刺协方差矩阵的上界，schattenq范数是一种特殊类型的酉不变范数。本文还讨论了在任意一元不变范数下，真尖形协方差矩阵与具有微分隐私的协方差矩阵之间的误差。除了高斯和亚高斯总体之外，我们还建立了有界亚高斯分布的上界，这是对Cai、Xia和Zha提供的高斯和亚高斯情况的补充。结果是我们的估计在某种程度上更好。

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Upper bounds of spiked covariance matrices under differentially private constrains

Cai, Xia, and Zha (2024) presented upper bounds of spiked covariance matrices for Gaussian and sub-Gaussian distributions under the Schatten-q norm, which is a particular type of unitarily invariant norm. In this paper, we also focus on the errors between the true spiked covariance matrices and the covariance matrices with differential privacy under any unitarily invariant norm. Beyond Gaussian and sub-Gaussian populations, we also establish the upper bound of the bounded sub-Gaussian distribution, which is a supplement to the Gaussian and sub-Gaussian cases provided by Cai, Xia, and Zha. It turns out that our estimations are better in some sense.

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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.