Research map / Adversarial robustness and security / Certified and empirical robustness
Sharp Statistical Guaratees for Adversarially Robust Gaussian Classification
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the plug-in estimator based on empirical mean and covariance | Adversarially robust Gaussian classification · Conditional Gaussian model, AdvSNR r | excess robust risk: O_P\Big(e^{-\frac{1}{8} r^2} \cdot r \cdot \frac{d}{n}\Big) | Helped |
| Restrict estimators to the paper's setting and distribution class | Adversarially robust Gaussian classification · Conditional Gaussian models with AdvSNR r | minimax excess robust risk: \Omega_P \Big(e^{-(\frac{1}{8} + o(1))r^2} \frac{d}{n} \Big) | Hurt |
| Replace the sample covariance with the true covariance (ablation) | Plug-in estimator for adversarially robust Gaussian classification · Conditional Gaussian model, AdvSNR r, known covariance | excess robust risk upper bound: O_P\left(e^{-\frac{1}{8} r^2} \cdot r \cdot \frac{d}{n}\right) -> O_P\left(e^{-\frac{1}{8} r^2} \cdot \frac{1}{r} \cdot | Helped |
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