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Version 4 changes:
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-- Version published in GAFA. Many typos fixed. (8/25/2015)
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Version 3 changes:
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-- Added a new co-author (Sjoerd Dirksen). (12/22/2014)
-- Generally polished things throughout the paper. (12/22/2014)
-- Put failure probability information in Section 4. This could be done
throughout the paper, but we didn't since after seeing how it's done
in Section 4, one will see the steps; there are no further conceptual
hurdles. (12/22/2014)
-- Added Section 3 (proof overview). (12/22/2014)
-- Fixed a cell in Figure 1 for "previous m" for collection of subspaces.
Previous work achieved d*log^6, not d+log^6. (12/22/2014)
-- Added some appendices to give background on topics that might be unfamiliar
to a TCS audience. (12/22/2014)
-- Added Section 6 on sketching constrained least squares with the SJLT.
(12/22/2014)
-- In Version 2 the sentence fragment
"We assume henceforth $k \le m/s$ since otherwise the integral above is $O(\sqrt{\log n})$"
above (6.14) is erroneous. This is replaced by something that actually makes
sense in Version 3 (namely (7.15)). (12/22/2014)
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Version 2 changes:
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-- Added more applications, to finite collections of (incoherent) subspaces,
with applications to model-based compressed sensing, as well as to infinite
collections of subspaces and smooth manifolds, with applications to manifold
learning. (4/2/2014)