Statistical Inference and Privacy, Part II

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" summary

Differential privacy is applied to classical statistical tasks with concrete costs and fixes: identity testing needs Θ(√K/γ^2) samples nonprivately but privacy adds extra terms or a multiplicative 1/ε factor via subsample-and-aggregate; privatizing counts with Laplace/Gaussian noise preserves asymptotic chi-squared test behavior but breaks finite-sample significance unless thresholds are recalibrated by Monte Carlo or analytic corrections; clipping the log-likelihood and adding Laplace noise yields private simple-hypothesis tests; L∞ estimation incurs a √d privacy penalty versus log d nonprivately.

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" chapters (23)

1. 0:00Private Statistics: A TCS Perspective
2. 0:56Outline
3. 1:29Algorithms vs. Statistics
4. 5:48Why Worst-Case Privacy?
5. 11:26"Utility"?
6. 13:56The Cost of Privacy
7. 14:45Asymptotic: One word, two meanings
8. 21:43Sample Complexity" versus "Rates
9. 25:06Classical Hypothesis Testing • Goal: If the H, holds (p = Ux), probability of "rejecting" is sa
10. 27:24Non-private: Pearson's Chi-squared Test
11. 34:26Privatizing the Chi-Squared Testing [Gaboardi-Lim-Rogers-Vadhan '16]
12. 37:54Minimax Hypothesis Testing
13. 40:04An minimax-optimal non-private test
14. 42:04Subsample and Aggregate [Nissim-Raskhodnikova-Smith '07]
15. 46:25Even Better Tests!
16. 48:42Private Distribution Estimation
17. 52:09Univariate Learning: Gaussians
18. 53:04Multivariate Learning: Product Distributions
19. 55:42Multivariate Learning: Gaussians
20. 56:02Distribution Learning vs. Reconstruction
21. 56:14Distribution Learning vs. Linear Queries
22. 56:35Distributional Functional Estimation
23. 59:13Private Simple Hypothesis Testing

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