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.APPROX/RANDOM.2020.12
URN: urn:nbn:de:0030-drops-126150
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12615/
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Phillips, Jeff M. ; Tai, Wai Ming

The GaussianSketch for Almost Relative Error Kernel Distance

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LIPIcs-APPROX12.pdf (0.7 MB)

Abstract

We introduce two versions of a new sketch for approximately embedding the Gaussian kernel into Euclidean inner product space. These work by truncating infinite expansions of the Gaussian kernel, and carefully invoking the RecursiveTensorSketch [Ahle et al. SODA 2020]. After providing concentration and approximation properties of these sketches, we use them to approximate the kernel distance between points sets. These sketches yield almost (1+ε)-relative error, but with a small additive α term. In the first variants the dependence on 1/α is poly-logarithmic, but has higher degree of polynomial dependence on the original dimension d. In the second variant, the dependence on 1/α is still poly-logarithmic, but the dependence on d is linear.

BibTeX - Entry

@InProceedings{phillips_et_al:LIPIcs:2020:12615,
  author =	{Jeff M. Phillips and Wai Ming Tai},
  title =	{{The GaussianSketch for Almost Relative Error Kernel Distance}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{12:1--12:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Jaros{\l}aw Byrka and Raghu Meka},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12615},
  URN =		{urn:nbn:de:0030-drops-126150},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.12},
  annote =	{Keywords: Kernel Distance, Kernel Density Estimation, Sketching}
}

Keywords: Kernel Distance, Kernel Density Estimation, Sketching
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)
Issue Date: 2020
Date of publication: 11.08.2020

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