Research map / Learning theory and algorithms / Matrix and tensor methods
Leveraging Well-Conditioned Bases: Streaming and Distributed Summaries in Minkowski $p$-Norms
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use an ℓ1- or ℓ2-conditioned basis to select high-leverage rows instead of the Identity method | ℓ∞-regression streaming summaries · US Census Data | approximation error | Helped |
| Use an ℓ1- or ℓ2-conditioned basis to select high-leverage rows instead of the Identity method | ℓ∞-regression streaming summaries · YearPredictionMSD | approximation error | Helped |
| Use an ℓ1- or ℓ2-conditioned basis to select high-leverage rows instead of uniform sampling | ℓ∞-regression streaming summaries · US Census Data | approximation error | Mixed |
| Use an ℓ1- or ℓ2-conditioned basis to select high-leverage rows instead of uniform sampling | ℓ∞-regression streaming summaries · YearPredictionMSD | approximation error | Helped |
| Use an orthonormal ℓ2 basis instead of an ℓ1-well-conditioned basis (ablation) | ℓ∞-regression streaming summaries · US Census Data | approximation error | Mixed |
| Use an orthonormal ℓ2 basis instead of an ℓ1-well-conditioned basis (ablation) | ℓ∞-regression streaming summaries · YearPredictionMSD | approximation error | No clear effect |
| Use the Identity method without conditioning instead of a well-conditioned basis (ablation) | ℓ∞-regression streaming summaries · US Census Data and YearPredictionMSD | approximation error | Hurt |
| Uniformly sample rows instead of selecting high-leverage rows with a well-conditioned basis (ablation) | ℓ∞-regression streaming summaries · US Census Data and YearPredictionMSD | summary size | Hurt |
| Use SPC1++ instead of SPC3 to compute the basis (ablation) | High-leverage row selection · Dense YearPredictionMSD data | computation time | Helped |
| Use SPC1++ instead of SPC3 to compute the basis (ablation) | High-leverage row selection · Streaming summary | summary size | Hurt |
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