One-Bit Compressed Sensing via One-Shot Hard Thresholding

Jie Shen
Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), PMLR 124:510-519, 2020.

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.

Cite this Paper


BibTeX
@InProceedings{pmlr-v124-shen20b, title = {One-Bit Compressed Sensing via One-Shot Hard Thresholding}, author = {Shen, Jie}, booktitle = {Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI)}, pages = {510--519}, year = {2020}, editor = {Jonas Peters and David Sontag}, volume = {124}, series = {Proceedings of Machine Learning Research}, month = {03--06 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v124/shen20b/shen20b.pdf}, url = { http://proceedings.mlr.press/v124/shen20b.html }, 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.} }
Endnote
%0 Conference Paper %T One-Bit Compressed Sensing via One-Shot Hard Thresholding %A Jie Shen %B Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI) %C Proceedings of Machine Learning Research %D 2020 %E Jonas Peters %E David Sontag %F pmlr-v124-shen20b %I PMLR %P 510--519 %U http://proceedings.mlr.press/v124/shen20b.html %V 124 %X 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.
APA
Shen, J.. (2020). One-Bit Compressed Sensing via One-Shot Hard Thresholding. Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI), in Proceedings of Machine Learning Research 124:510-519 Available from http://proceedings.mlr.press/v124/shen20b.html .

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