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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2022.51

One-Pass Additive-Error Subset Selection for 𝓁_p Subspace Approximation

Authors: Amit Deshpande and Rameshwar Pratap

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract

We consider the problem of subset selection for 𝓁_p subspace approximation, that is, to efficiently find a small subset of data points such that solving the problem optimally for this subset gives a good approximation to solving the problem optimally for the original input. Previously known subset selection algorithms based on volume sampling and adaptive sampling [Deshpande and Varadarajan, 2007], for the general case of p ∈ [1, ∞), require multiple passes over the data. In this paper, we give a one-pass subset selection with an additive approximation guarantee for 𝓁_p subspace approximation, for any p ∈ [1, ∞). Earlier subset selection algorithms that give a one-pass multiplicative (1+ε) approximation work under the special cases. Cohen et al. [Michael B. Cohen et al., 2017] gives a one-pass subset section that offers multiplicative (1+ε) approximation guarantee for the special case of 𝓁₂ subspace approximation. Mahabadi et al. [Sepideh Mahabadi et al., 2020] gives a one-pass noisy subset selection with (1+ε) approximation guarantee for 𝓁_p subspace approximation when p ∈ {1, 2}. Our subset selection algorithm gives a weaker, additive approximation guarantee, but it works for any p ∈ [1, ∞).

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Amit Deshpande and Rameshwar Pratap. One-Pass Additive-Error Subset Selection for 𝓁_p Subspace Approximation. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 51:1-51:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{deshpande_et_al:LIPIcs.ICALP.2022.51,
  author =	{Deshpande, Amit and Pratap, Rameshwar},
  title =	{{One-Pass Additive-Error Subset Selection for 𝓁\underlinep Subspace Approximation}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{51:1--51:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.51},
  URN =		{urn:nbn:de:0030-drops-163924},
  doi =		{10.4230/LIPIcs.ICALP.2022.51},
  annote =	{Keywords: Subspace approximation, streaming algorithms, low-rank approximation, adaptive sampling, volume sampling, subset selection}
}

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1 Search Results for "Pratap, Rameshwar"

One-Pass Additive-Error Subset Selection for 𝓁_p Subspace Approximation

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