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We introduce three differentially-private algorithms that approximates the2nd-moment matrix of the data. These algorithm, which in contrast to existingalgorithms output positive-definite matrices, correspond to existing techniquesin linear regression literature. Specifically, we discuss the following threetechniques. (i) For Ridge Regression, we propose setting the regularizationcoefficient so that by approximating the solution using Johnson-Lindenstrausstransform we preserve privacy. (ii) We show that adding a small batch of randomsamples to our data preserves differential privacy. (iii) We show that samplingthe 2nd-moment matrix from a Bayesian posterior inverse-Wishart distribution isdifferentially private provided the prior is set correctly. We also evaluateour techniques experimentally and compare them to the existing "Analyze Gauss"algorithm of Dwork et al.

Private Approximations of the 2nd-Moment Matrix Using Existing Techniques in Linear Regression