Research map / Learning theory and algorithms / Sample complexity
Local Density Estimation in High Dimensions
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use LSH Count with sampling from nonzero Hamming-distance buckets instead of enumerating only distance-0 buckets | LSH-based density estimation · GloVe, Venice, Cake, and Book (0–60°) | relative error: within 20% vs higher than 50% | Helped |
| Add importance weighting to query-directed multi-probe (ablation) | Multi-Probe Count · GloVe, Venice, Cake, and Book (0–60°), 1000 inspected elements | relative error | Helped |
| Add importance weighting to query-directed multi-probe (ablation) | Multi-Probe Count · GloVe, Cake and Book (0–60°), 5000 inspected elements | relative error | Helped |
| Add importance weighting to query-directed multi-probe (ablation) | Multi-Probe Count · GloVe, Venice (0–60°), 5000 inspected elements and more than 10 tables | relative error: 1 or 2 percentage points | Mixed |
| Increase the LSH Count sampling Hamming threshold (ablation) | LSH Count · GloVe queries | inherent bias: under 10% | Helped |
| Increase the LSH Count sampling Hamming threshold (ablation) | LSH Count · GloVe queries | sample complexity | Hurt |
| Use Hamming thresholds farther from the query bucket (ablation) | LSH Count · GloVe queries | estimate quality | Hurt |
| Choose LSH Count rather than Multi-Probe Count | Local density estimation · GloVe, Venice (sparse neighborhood) | relative error | Hurt |
| Choose LSH Count rather than Multi-Probe Count | Local density estimation · GloVe, Book (dense neighborhood) | relative error | Helped |
| Choose LSH Count with a suitable Hamming threshold rather than Multi-Probe Count | Local density estimation · GloVe, Cake (medium-sized neighborhood) | relative error | Helped |
| Rank multi-probe buckets using target angles of 30°, 45°, or 60° (ablation) | Multi-Probe · GloVe queries | relative error | No clear effect |
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