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Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2022.51
URN: urn:nbn:de:0030-drops-163924
URL: https://drops.dagstuhl.de/opus/volltexte/2022/16392/
Deshpande, Amit ;
Pratap, Rameshwar
One-Pass Additive-Error Subset Selection for 𝓁_p Subspace Approximation
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, ∞).
BibTeX - Entry
@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.dagstuhl.de/opus/volltexte/2022/16392},
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}
}
Keywords: |
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Subspace approximation, streaming algorithms, low-rank approximation, adaptive sampling, volume sampling, subset selection |
Collection: |
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49th International Colloquium on Automata, Languages, and Programming (ICALP 2022) |
Issue Date: |
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2022 |
Date of publication: |
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28.06.2022 |