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Kernel Density Estimation through Density Constrained Near Neighbor Search
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- 1 Intro
- 2 Kernel Functions
- 3 Kernel Density
- 4 Motivation
- 5 A A Trivial Solution
- 6 Analysis of Random Sampling
- 7 Prior Work and Our Result
- 8 Can we do better than random sampling?
- 9 Importance Sampling Estimator
- 10 Locality Sensitive Hashing (LSH)
- 11 Charikar-Siminelakis'17
- 12 Some Simplifying Assumptions
- 13 Ideal Importance Sampling
- 14 Our Approach
- 15 Using Andoni-Indyk LSH for Recovery
- 16 Collision Probabilities
- 17 Density Constraints
- 18 Size of Query's Bucket (Simplified)
- 19 Size of Query's Bucket (Detailed)
- 20 Query Time
- 21 Space
- 22 Basics of Data Dependent LSH
- 23 General Approach in Data Dependent LSH
- 24 Log-Density
- 25 Density Evolution of Query's Bucket
- 26 Effect of Hashing on Log-Densities
- 27 Technical Steps
- 28 Open Questions
