eng
Schloss Dagstuhl β Leibniz-Zentrum fΓΌr Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-06-28
51:1
51:14
10.4230/LIPIcs.ICALP.2022.51
article
One-Pass Additive-Error Subset Selection for π_p Subspace Approximation
Deshpande, Amit
1
Pratap, Rameshwar
2
Microsoft Research, Bengaluru, India
Indian Institute of Technology, Mandi, H.P., India
We consider the problem of subset selection for π_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 β [1, β), require multiple passes over the data. In this paper, we give a one-pass subset selection with an additive approximation guarantee for π_p subspace approximation, for any p β [1, β). Earlier subset selection algorithms that give a one-pass multiplicative (1+Ξ΅) 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+Ξ΅) approximation guarantee for the special case of πβ subspace approximation. Mahabadi et al. [Sepideh Mahabadi et al., 2020] gives a one-pass noisy subset selection with (1+Ξ΅) approximation guarantee for π_p subspace approximation when p β {1, 2}. Our subset selection algorithm gives a weaker, additive approximation guarantee, but it works for any p β [1, β).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol229-icalp2022/LIPIcs.ICALP.2022.51/LIPIcs.ICALP.2022.51.pdf
Subspace approximation
streaming algorithms
low-rank approximation
adaptive sampling
volume sampling
subset selection