Research map / Learning theory and algorithms / Sample complexity
List-Decodable Mean Estimation in Nearly-PCA Time
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace sequential cluster finding with subspace identification followed by simultaneous low-dimensional clustering | List-decodable mean estimation · List-decodable mean estimation | runtime: \widetilde{O}(n^2 d k^2) -> \widetilde{O}\Par{\frac{nd}{\alpha} + \frac{1}{\alpha^6}} | Helped |
| use the random-sampling postprocessing variant (ablation) | ListDecodableMeanEstimation · List-decodable mean estimation | runtime: \widetilde{O}\Par{\frac{nd}{\alpha} + \frac{1}{\alpha^6}} -> \widetilde{O}\Par{\frac{nd}{\alpha}} | Helped |
| use the random-sampling postprocessing variant (ablation) | ListDecodableMeanEstimation · List-decodable mean estimation | mean error: O \left(\sigma \sqrt{\tfrac{1}{\alpha}}\right) -> O \left(\sigma \sqrt{\tfrac{\log \alpha^{-1}}{\alpha}}\right) | Hurt |
| use iterative soft downweighting with whitened top-k eigenspace scores and saturation | SIFT · List-decodable mean estimation | mean error squared: Theorem guarantees \frac{22}{\alpha} | Helped |
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