Abstract
Given a point set P ⊂ ℝ^d, the kernel density estimate of P is defined as
?-_P(x) = 1/|P| ∑_{p ∈ P}e^{-∥x-p∥²}
for any x ∈ ℝ^d. We study how to construct a small subset Q of P such that the kernel density estimate of P is approximated by the kernel density estimate of Q. This subset Q is called a coreset. The main technique in this work is constructing a ± 1 coloring on the point set P by discrepancy theory and we leverage Banaszczyk’s Theorem. When d > 1 is a constant, our construction gives a coreset of size O(1/ε) as opposed to the best-known result of O(1/ε √{log 1/ε}). It is the first result to give a breakthrough on the barrier of √log factor even when d = 2.
BibTeX - Entry
@InProceedings{tai:LIPIcs.SoCG.2022.63,
author = {Tai, Wai Ming},
title = {{Optimal Coreset for Gaussian Kernel Density Estimation}},
booktitle = {38th International Symposium on Computational Geometry (SoCG 2022)},
pages = {63:1--63:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-227-3},
ISSN = {1868-8969},
year = {2022},
volume = {224},
editor = {Goaoc, Xavier and Kerber, Michael},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16071},
URN = {urn:nbn:de:0030-drops-160719},
doi = {10.4230/LIPIcs.SoCG.2022.63},
annote = {Keywords: Discrepancy Theory, Kernel Density Estimation, Coreset}
}
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Keywords: |
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Discrepancy Theory, Kernel Density Estimation, Coreset |
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Collection: |
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38th International Symposium on Computational Geometry (SoCG 2022) |
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Issue Date: |
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2022 |
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Date of publication: |
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01.06.2022 |
Creative Commons Attribution 4.0 International license (CC BY 4.0)