Research map / Federated learning and privacy / Differential privacy
Differentially Private Distributed Bayesian Linear Regression with MCMC
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| fixing S to nearest PSD estimate (MCMC-fixedS / Bayes-fixedS-fast) instead of sampling S (ablation) | proposed Bayesian linear regression under DP · BikeSharing and AirQuality, J=5 and J=10 (real data, eps=1) | prediction MSE: e.g. BikeSharing J=10: 0.0812 -> 0.0082 | Helped |
| distributed setting (J=5, 10) with proposed methods vs J=1 | MCMC-normalX · BikeSharing real data, eps=1 | prediction MSE: 0.0024 (J=1) -> 0.0812 (J=10) | Hurt |
| proposed fixed-S methods vs adaSSP in the distributed setting | MCMC-fixedS / Bayes-fixedS-fast · real datasets, eps=1, J>1 | prediction MSE: e.g. PowerPlant J=10: 0.0351 (adaSSP) -> 0.0143 | Helped |
| proposed methods vs MCMC-B&S on real data at J=1 | proposed methods · PowerPlant, BikeSharing, eps=1, J=1 | prediction MSE: MCMC-B&S slightly better (0.0128 vs 0.0129; 0.0020 vs 0.0021) | No clear effect |
| Bayesian proposed methods vs MCMC-B&S on simulated data at d=2 vs d=5 | MCMC-normalX vs MCMC-B&S · simulated, n=1e5 | MSE | Mixed |
| avoid releasing extra y^T y statistic (proposed model vs MCMC-B&S) | proposed hierarchical model · simulated data, d=2 | MSE | Helped |
| proposed MCMC vs MCMC-B&S per-iteration cost (O(d^3) vs O(d^6)) | MCMC algorithms · run time vs d | run time per iteration | Helped |
| fixed-S methods vs adaSSP on simulated data across J and epsilon | MCMC-fixedS and Bayes-fixedS-fast · simulated n=1e5, d=2 and d=5, J in {1,5,10} | estimation and prediction MSE | Helped |
| increasing privacy budget epsilon | all methods · simulated data | MSE and MMD | Helped |
| averaging features to approximate normality (adding CLT averaging) | proposed methods · not evaluated empirically | n/a | No clear effect |
| 3droad dataset, all methods | all methods · 3droad, J=1,5,10, eps=1 | prediction MSE: 0.0229 for all methods | No clear effect |
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