Overview
Syllabus
Intro
Kernel Functions
Kernel Density
Motivation
A A Trivial Solution
Analysis of Random Sampling
Prior Work and Our Result
Can we do better than random sampling?
Importance Sampling Estimator
Locality Sensitive Hashing (LSH)
Charikar-Siminelakis'17
Some Simplifying Assumptions
Ideal Importance Sampling
Our Approach
Using Andoni-Indyk LSH for Recovery
Collision Probabilities
Density Constraints
Size of Query's Bucket (Simplified)
Size of Query's Bucket (Detailed)
Query Time
Space
Basics of Data Dependent LSH
General Approach in Data Dependent LSH
Log-Density
Density Evolution of Query's Bucket
Effect of Hashing on Log-Densities
Technical Steps
Open Questions
Taught by
IEEE FOCS: Foundations of Computer Science