Research map / Learning theory and algorithms / Sample complexity
Being Robust (in High Dimensions) Can Be Practical
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the proposed Filter instead of LRVCov | Robust covariance estimation · Synthetic covariance, isotropic and skewed settings | excess Mahalanobis error: our excess error was on the order of $10^{-4}$; LRVCov's was in all cases a constant between $0.1$ and $2$ | Helped |
| Use Filter instead of empirical mean, pruning, geometric median, or RANSAC | Robust mean estimation · Synthetic mean | excess ℓ2 error | Helped |
| Use Filter instead of empirical covariance, pruning, or RANSAC | Robust covariance estimation · Synthetic covariance | excess Mahalanobis error | Helped |
| Use adaptive tail bounding rather than a fixed tail threshold (ablation) | Filter for robust covariance estimation · Synthetic covariance | estimation accuracy | Helped |
| Center projected points at the median instead of the empirical mean (ablation) | Filter for robust mean estimation · Robust mean estimation | estimation error | Helped |
| Apply Filter rather than pruning to the noisy genetic dataset | Robust covariance estimation and PCA · POPRES genetic data with added noise | qualitative recovery of the Europe map | Helped |
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