基于差分隐私度序列研究瑟斯顿模型中参数估计量的渐近性理论
Asymptotics in Thurstone model for natworks with a differentially private degree sequence
投稿时间:2022-03-10  修订日期:2022-03-10
DOI:
中文关键词: 瑟斯顿模型  相合性  渐近正态性  差分隐私
英文关键词: Thurstone model  asymptotic normality  consistency  differential privacy
基金项目:中央专项基金青年基金(CZQ19010)
作者单位邮编
胡军浩 中南民族大学 数学与统计学学院 
马晓慧 中南民族大学 数学与统计学学院 
罗敬 中南民族大学 数学与统计学学院 430074
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中文摘要:
      瑟斯顿模型主要用于研究成对数据比较问题的统计模型.该模型在心理测量,社交选择,推荐系统等方面有着广泛的应用.然而,由于心理学研究中常常获取包含着个人隐私的数据,直接将数据发布进行分析会带来隐私泄露的风险,因此数据隐私保护显得尤为重要.本文通过对原始数据加入离散拉普拉斯噪声进行加密,然后利用数理统计的方法建立了带有噪声的瑟斯顿模型参数的渐近性理论.最后,我们利用数值模拟验证了理论结果.
英文摘要:
      Thurstone model is mainly used to study the statistical model of pairwise comparison problem .The model has a wide range of applications in psychological measurement, social choice, recommendation system and so on. However, because psychological research often obtains data containing personal privacy, directly publishing and analyzing the data will bring the risk of privacy disclosure, so data privacy protection is particularly important. This paper encrypts the original data with discrete Laplace noise, and then establishes the asymptotic theory of the parameters of Thurstone model with noise by using the method of mathematical statistics. Finally, we verify the theoretical results by numerical simulation.
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