Abstract
An oblivious subspace embedding (OSE) for some ε,δ ∈(0,1/3) and d ≤ m ≤ n is a distribution D over ℝmxn such that (Equation Presented) for any linear subspace W ⊂ ℝn of dimension d. We prove any OSE with δ < 1/3 has m = Ω((d + log(1/δ))/ε2), which is optimal. Furthermore, if every Π in the support of is sparse, having at most s non-zero entries per column, we show tradeoff lower bounds between m and s. © 2014 Springer-Verlag.
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CITATION STYLE
Nelson, J., & Nguyên, H. L. (2014). Lower bounds for oblivious subspace embeddings. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8572 LNCS, pp. 883–894). Springer Verlag. https://doi.org/10.1007/978-3-662-43948-7_73
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