License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2018.66
URN: urn:nbn:de:0030-drops-87797
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Phillips, Jeff M. ; Tai, Wai Ming

Near-Optimal Coresets of Kernel Density Estimates

LIPIcs-SoCG-2018-66.pdf (0.6 MB)


We construct near-optimal coresets for kernel density estimate for points in R^d when the kernel is positive definite. Specifically we show a polynomial time construction for a coreset of size O(sqrt{d log (1/epsilon)}/epsilon), and we show a near-matching lower bound of size Omega(sqrt{d}/epsilon). The upper bound is a polynomial in 1/epsilon improvement when d in [3,1/epsilon^2) (for all kernels except the Gaussian kernel which had a previous upper bound of O((1/epsilon) log^d (1/epsilon))) and the lower bound is the first known lower bound to depend on d for this problem. Moreover, the upper bound restriction that the kernel is positive definite is significant in that it applies to a wide-variety of kernels, specifically those most important for machine learning. This includes kernels for information distances and the sinc kernel which can be negative.

BibTeX - Entry

  author =	{Jeff M. Phillips and Wai Ming Tai},
  title =	{{Near-Optimal Coresets of Kernel Density Estimates}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{66:1--66:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-87797},
  doi =		{10.4230/LIPIcs.SoCG.2018.66},
  annote =	{Keywords: Coresets, Kernel Density Estimate, Discrepancy}

Keywords: Coresets, Kernel Density Estimate, Discrepancy
Collection: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 08.06.2018

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