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Leveraging Well-Conditioned Bases: Streaming and Distributed Summaries in Minkowski $p$-Norms
Charlie Dickens · Graham Cormode · David Woodruff

Wed Jul 11 04:30 AM -- 04:50 AM (PDT) @ K11
Work on approximate linear algebra has led to efficient distributed and streaming algorithms for problems such as approximate matrix multiplication, low rank approximation, and regression, primarily for the Euclidean norm $\ell_2$. We study other $\ell_p$ norms, which are more robust for $p < 2$, and can be used to find outliers for $p > 2$. Unlike previous algorithms for such norms, we give algorithms that are (1) deterministic, (2) work simultaneouslyfor every $p \geq 1$, including $p = \infty$, and (3) can be implemented in both distributed and streaming environments. We study $\ell_p$-regression, entrywise $\ell_p$-low rank approximation, and versions of approximate matrix multiplication.

Author Information

Charlie Dickens (Alan Turing Institute & University of Warwick)
Graham Cormode (University of Warwick)
David Woodruff (Carnegie Mellon University)

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