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 `2-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 language | English |
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Pages | 510-519 |
Number of pages | 10 |
State | Published - 2020 |
Event | 36th Conference on Uncertainty in Artificial Intelligence, UAI 2020 - Virtual, Online Duration: 3 Aug 2020 → 6 Aug 2020 |
Conference
Conference | 36th Conference on Uncertainty in Artificial Intelligence, UAI 2020 |
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City | Virtual, Online |
Period | 3/08/20 → 6/08/20 |