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Research map / Learning theory and algorithms / Sample complexity

Local Density Estimation in High Dimensions

ICML 2018 · Learning theory and algorithms › Sample complexity · approach: Density and property estimation · 6 citations (OpenAlex)

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Use LSH Count with sampling from nonzero Hamming-distance buckets instead of enumerating only distance-0 bucketsLSH-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 elementsrelative errorHelped
Add importance weighting to query-directed multi-probe (ablation)Multi-Probe Count · GloVe, Cake and Book (0–60°), 5000 inspected elementsrelative errorHelped
Add importance weighting to query-directed multi-probe (ablation)Multi-Probe Count · GloVe, Venice (0–60°), 5000 inspected elements and more than 10 tablesrelative error: 1 or 2 percentage pointsMixed
Increase the LSH Count sampling Hamming threshold (ablation)LSH Count · GloVe queriesinherent bias: under 10%Helped
Increase the LSH Count sampling Hamming threshold (ablation)LSH Count · GloVe queriessample complexityHurt
Use Hamming thresholds farther from the query bucket (ablation)LSH Count · GloVe queriesestimate qualityHurt
Choose LSH Count rather than Multi-Probe CountLocal density estimation · GloVe, Venice (sparse neighborhood)relative errorHurt
Choose LSH Count rather than Multi-Probe CountLocal density estimation · GloVe, Book (dense neighborhood)relative errorHelped
Choose LSH Count with a suitable Hamming threshold rather than Multi-Probe CountLocal density estimation · GloVe, Cake (medium-sized neighborhood)relative errorHelped
Rank multi-probe buckets using target angles of 30°, 45°, or 60° (ablation)Multi-Probe · GloVe queriesrelative errorNo clear effect

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