A Quasi-Monte Carlo Algorithm for Smooth Kernel Evaluation

Explore a 42-minute lecture on a novel Quasi-Monte Carlo algorithm for smooth kernel evaluation presented by Erik Waingarten from the University of Pennsylvania. Delve into the development of a data structure for density queries that approximates the sum of pairwise kernel evaluations given a dataset of vectors and a kernel function. Discover how this research combines discrepancy theory and Locality-Sensitive Hashing (LSH) to create sparse coresets and enhance existing data structures for smooth kernels. Learn about the integration of two research approaches from Backurs, Indyk, Charikar, Siminelakis (2018) and Phillips and Tai (2019), showcasing how to achieve optimal results from both. Gain insights into the collaborative work with Moses Charikar and Michael Kapralov, as presented in their arxiv paper. This talk, part of the Sublinear Graph Simplification series at the Simons Institute, offers a deep dive into advanced algorithms for efficient kernel evaluation in high-dimensional spaces.