差异化隐私预算分配的线性回归分析算法

摘要

针对用差分隐私方法进行线性回归分析敏感性偏大的问题，提出一种差异化的隐私预算分配算法 Diff-LR（Differential Privacy Linear Regression）。该算法首先把目标函数分解成两个子函数，再分别计算两个子函数的敏感性、分配合理的隐私预算，并采用拉普拉斯机制给两个子函数系数添加噪音。然后对子函数进行组合，得到添加噪声后的目标函数，求取最优线性回归模型参数。最后利用差分隐私序列组合特性从理论上证明该算法满足ε-差分隐私。实验结果表明，Diff-LR 算法产生的线性回归模型具有很高的预测准确性。%For the problem of relatively big sensitivity when using differential privacy method to make linear regression analysis,this paper puts forward the differential privacy budget allocation algorithm-Diff-LR.First,the algorithm divides the objective function into two sub-func-tions,then calculates the sensitivities of them separately and allocates reasonable privacy budget to them,as well as uses Laplace transform mechanism to add noises to the coefficients of them.After that,it combines these two sub-functions,and gets the objective function with the noise added.Then it calculates the optimal linear regression parameters,and finally employs the characteristic of differential privacy sequence combination to prove theoretically this algorithm satisfies ε-differential privacy.Experimental results show that the linear regression model generated by Diff-LR has high predictive accuracy.