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2016
ACM

Nearly-optimal bounds for sparse recovery in generic norms, with applications to k-median sketching

3 years 8 months ago
Nearly-optimal bounds for sparse recovery in generic norms, with applications to k-median sketching
We initiate the study of trade-offs between sparsity and the number of measurements in sparse recovery schemes for generic norms. Specifically, for a norm · , sparsity parameter k, approximation factor K > 0, and probability of failure P > 0, we ask: what is the minimal value of m so that there is a distribution over m × n matrices A with the property that for any x, given Ax, we can recover a k-sparse approximation to x in the given norm with probability at least 1 − P? We give a partial answer to this problem, by showing that for norms that admit efficient linear sketches, the optimal number of measurements m is closely related to the doubling dimension of the metric induced by the norm · on the set of all k-sparse vectors. By applying our result to specific norms, we cast known measurement bounds in our general framework (for the p norms, p ∈ [1, 2]) as well as provide new, measurementefficient schemes (for the Earth-Mover Distance norm). The latter result directly ...
Arturs Backurs, Piotr Indyk, Ilya Razenshteyn, Dav
Added 09 Apr 2016
Updated 09 Apr 2016
Type Journal
Year 2016
Where SODA
Authors Arturs Backurs, Piotr Indyk, Ilya Razenshteyn, David P. Woodruff
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