Research map / Federated learning and privacy / Differential privacy
Wishart Mechanism for Differentially Private Principal Components Analysis
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Wishart noise instead of symmetric entrywise Laplace noise | Input perturbation for differentially private PCA · Covariance matrix publishing (PCA) | spectral norm of noise: O(d\sqrt{d}/n\epsilon) -> O(d\log d/n\epsilon) | Helped |
| Add Wishart noise to the covariance matrix | Wishart mechanism · Covariance matrix publishing (PCA) | positive semi-definiteness | Helped |
| Use Wishart input perturbation under the paper's adjacency definition | PCA · PCA top-k subspace | Frobenius subspace error: \frac{2\sqrt{k}\norm{W}_2}{\sigma_{k}-\sigma_{k+1}} | Helped |
| Use Wishart mechanism for rank-k approximation | Private low-rank approximation · Rank-k approximation | spectral norm approximation error: O(\frac{k^3 d}{\epsilon}) -> O(\frac{d\log d}{\epsilon}) | Helped |
| Use Wishart mechanism instead of the meta algorithm | Private low-rank approximation · Rank-k approximation | spectral norm approximation error: O(\frac{k^{\frac{3}{2}}d\log^2 d }{\epsilon}) -> O(\frac{d\log d}{\epsilon}) | Helped |
| Use Wishart mechanism rather than the rank-k exponential/Laplace algorithm | Private low-rank approximation · Rank-k approximation | running time: O(d^6/\epsilon) -> O(kd^2) | Helped |
| Choose Wishart rather than Laplace when the sensitivity ratio exceeds the stated threshold | Symmetric matrix input perturbation · Covariance matrix publishing | spectral norm of noise: \omega(\sqrt{d}\log d) | Mixed |
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