Private Approximations of the 2nd-Moment Matrix Using Existing Techniques in Linear Regression
Private Approximations of the 2nd-Moment Matrix Using Existing Techniques in Linear Regression
复制标题
使用线性回归中的现有技术对二阶矩矩阵进行私有近似
DOI：
--
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Or Sheffet
中科院分区：
文献类型：
--
作者：
Or Sheffet
我们介绍了三个差分私有算法，近似的数据的二阶矩矩阵。这些算法，这在现有的算法输出正定矩阵，对应于现有的技术在线性回归文献。具体来说，我们将讨论以下三种技术。(i)对于岭回归，我们建议设置正则化系数，以便通过使用Johnson-Lindenstrauss变换来近似解决方案，从而保护隐私。(ii)我们表明，添加一小批随机样本到我们的数据保留差分隐私。(iii)我们发现，从贝叶斯后验逆Wishart分布的二阶矩矩阵的采样是差分私有的，前提是正确设置。我们还评估我们的技术实验，并将其与现有的“分析高斯”算法Dwork等人。
We introduce three differentially-private algorithms that approximates the 2nd-moment matrix of the data. These algorithm, which in contrast to existing algorithms output positive-definite matrices, correspond to existing techniques in linear regression literature. Specifically, we discuss the following three techniques. (i) For Ridge Regression, we propose setting the regularization coefficient so that by approximating the solution using Johnson-Lindenstrauss transform we preserve privacy. (ii) We show that adding a small batch of random samples to our data preserves differential privacy. (iii) We show that sampling the 2nd-moment matrix from a Bayesian posterior inverse-Wishart distribution is differentially private provided the prior is set correctly. We also evaluate our techniques experimentally and compare them to the existing "Analyze Gauss" algorithm of Dwork et al.