函数回归的差分隐私保护算法

Differential Privacy Preservation Algorithm in Functional Regression

函数型数据回归是一种特殊的回归分析,其响应或协变量包含函数型数据,即样本元素为连续函数的数据。函数型数据在医疗保健、社交媒体、传感网络等诸多领域都有重要应用,通常包含一些敏感信息,在回归分析的过程中,不加保护会引起隐私的泄露。针对函数型数据回归分析中缺少隐私保护的问题,提出了一种基于拉普拉斯机制的函数回归的差分隐私保护算法。首先,对响应数据进行降维,将响应函数建模为相互正交的B样条基的张量积,建立函数回归的数学模型;其次,对回归模型的未知参数取值使用惩罚最小二乘法估计,并通过正交基函数的数量控制粗糙度;最后,对估计参数加入服从拉普拉斯分布的噪声扰动,得到最终的回归结果。理论分析和实验表明,函数回归的差分隐私保护算法满足拉普拉斯机制的差分隐私保护,并且随着隐私预算的减小,算法效率越高,在保证数据安全性的同时达到了良好的可用性。

Functional data regression is a special kind of regression analysis whose responses or covariates contain functional data,that is,data whose sample elements are continuous functions.Functional data has important applications in many fields such as health care,social media,and sensor networks.It usually contains some sensitive information.In the process of regression analysis,if it is not protected,it will cause privacy leakage.Aiming at the lack of privacy protection in functional data regression analysis,a differential privacy protection algorithm based on Laplacian mechanism for functional regression is proposed.Firstly,reduce the dimension of the response data,model the response function as a tensor product of mutually orthogonal B-spline bases,and establish a mathematical model of function regression.Secondly,use the penalized least squares method for the unknown parameters of the regression model,and control the roughness through the number of orthogonal basis functions.Finally,add noise disturbance obeying Laplace distribution to the estimated parameters to obtain the final regression result.Theoretical analysis and experiments show that the differential privacy protection algorithm of functional regression satisfies the differential privacy protection of the Laplacian mechanism,and with the reduction of the privacy budget,the efficiency of the algorithm is higher,and it achieves excellent usability while ensuring data security.