Research map / Learning theory and algorithms / Prediction and decision losses
On Medians of (Randomized) Pairwise Means
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SRSWoR randomized blocks (MoRM, tau=9/20) instead of disjoint segmentation (MoM) | median-of-means mean estimation · Normal/Student/Log-normal mean estimation, n=1000 | quadratic risk: e.g. Normal 0.00149 -> 0.00105; Log-normal 0.00697 -> 0.00497 | Helped |
| Use SRSWoR randomized blocks with tau=9/20 instead of disjoint segmentation | median-of-means mean estimation · Pareto (3) mean estimation, n=1000 | quadratic risk: 1.02036 -> 1.02802 | No clear effect |
| Set tau=1/6 for MoRM (about same number of blocks as MoM, uses fewer samples) (ablation) | MoRM mean estimation · Normal (0,1) mean estimation, n=1000 | quadratic risk: 0.00149 -> 0.01366 | Hurt |
| Set tau=3/10 for MoRM (uses as many samples as MoM) (ablation) | MoRM mean estimation · Normal (0,1) mean estimation, n=1000 | quadratic risk: 0.00149 -> 0.00255 | Hurt |
| Use median of randomized U-statistics (SRSWoR blocks) instead of partition-based median of U-statistics | variance estimation via U-statistics · Normal/Student/Pareto variance estimation, n=1000 | quadratic risk: Normal 0.00324 -> 0.00504; Student 0.38242 -> 0.51202; Pareto 0.09300 -> 0.09703 | Hurt |
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