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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 09:15 AM -- 12:00 PM (PDT) @ Hall B #40
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 simultaneously for 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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