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Nguyen, Jelani Nelson","submitted_at":"2013-08-15T00:23:36Z","abstract_excerpt":"An oblivious subspace embedding (OSE) for some eps, delta in (0,1/3) and d <= m <= n is a distribution D over R^{m x n} such that for any linear subspace W of R^n of dimension d,\n  Pr_{Pi ~ D}(for all x in W, (1-eps) |x|_2 <= |Pi x|_2 <= (1+eps)|x|_2) >= 1 - delta.\n  We prove that any OSE with delta < 1/3 must have m = Omega((d + log(1/delta))/eps^2), which is optimal. 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