One-Bit Compressed Sensing via One-Shot Hard Thresholding

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Abstract

This paper concerns the problem of 1-bit compressed sensing, where the goal is to estimate a sparse signal from a few of its binary measurements. We study a non-convex sparsity-constrained program and present a novel and concise analysis that moves away from the widely used notion of Gaussian width. We show that with high probability a simple algorithm is guaranteed to produce an accurate approximation to the normalized signal of interest under the l2-metric. On top of that, we establish an ensemble of new results that address norm estimation, support recovery, and model misspecification. On the computational side, it is shown that the non-convex program can be solved via one-step hard thresholding which is dramatically efficient in terms of time complexity and memory footprint. On the statistical side, it is shown that our estimator enjoys a near-optimal error rate under standard conditions. The theoretical results are further substantiated by numerical experiments.

Original languageEnglish
Pages (from-to)510-519
Number of pages10
JournalProceedings of Machine Learning Research
Volume124
StatePublished - 2020
Event36th Conference on Uncertainty in Artificial Intelligence, UAI 2020 - Virtual, Online
Duration: 3 Aug 20206 Aug 2020

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