When Existing Techniques in Linear Regression Preserve Differential Privacy
summary
Shows that standard regressors already give differential privacy if applied to the second-moment matrix with the right randomness and scale. Releasing the covariance plus additive Wishart noise or outputting a draw from a Wishart/inverse-Wishart posterior is (ε,δ)-DP provided singular values exceed a threshold; niceness of the data replaces huge sample sizes. One-dimensional analysis sets degrees of freedom k roughly proportional to 1/ε^2 and uses chi-square concentration to bound the privacy loss.
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chapters (8)
- 0:00Introduction to DP
- 2:24Defining differential privacy
- 5:04Private linear regression
- 7:15Regularization and statistics
- 12:58Wishart distributions
- 16:02Privacy theorems
- 20:05Proof overview
- 29:14Discussion and Q&A
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