Research map / Learning theory and algorithms / Sample complexity
Optimal Analysis of Subset-Selection Based L_p Low-Rank Approximation
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use weighted averaging over all k-column subsets and Riesz-Thorin interpolation in the analysis | Column Subset Selection · ℓ_p rank-k approximation, 1≤p≤2 | approximation ratio: O(k+1) -> (k+1)^{1/p} | Helped |
| Use weighted averaging over all k-column subsets and Riesz-Thorin interpolation in the analysis | Column Subset Selection · ℓ_p rank-k approximation, p≥2 | approximation ratio: O(k+1) -> (k+1)^{1-1/p} | Helped |
| Apply the improved CSS analysis to select O(k log m) columns | SelectColumns bi-criteria algorithm · ℓ_p rank-k approximation | approximation ratio: O(k+1) -> O(c_{p,k}) | Helped |
| Apply the improved CSS analysis in the polynomial-time exact-rank construction | Polynomial-time exact-rank algorithm · ℓ_p rank-k approximation, k = O(log n/log log n) | approximation ratio: O(k^4 log(m)) -> O(c_{p,k}^3 k log m) | Helped |
| Require exactly k selected columns rather than O(k log m) selected columns | Column Subset Selection · ℓ_p rank-k approximation, p≥2 | approximation ratio: Upper bound (k+1)^{1-1/p}; lower bound (k+1)^{1-1/p} | Mixed |
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