Homomorphic Sensing: Sparsity and Noise

doi:none

	Homomorphic Sensing: Sparsity and Noise
	Liangzu Peng; Boshi Wang; Manolis Tsakiris
	2021
会议录名称	PROCEEDINGS OF THE 38TH INTERNATIONAL CONFERENCE ON MACHINE LEARNING
卷号	139
页码	8464-8475
发表状态	已发表
DOI	none
摘要	Unlabeled sensing is a recent problem encompassing many data science and engineering applications and typically formulated as solving linear equations whose right-hand side vector has undergone an unknown permutation. It was generalized to the homomorphic sensing problem by replacing the unknown permutation with an unknown linear map from a given finite set of linear maps. In this paper we present tighter and simpler conditions for the homomorphic sensing problem to admit a unique solution. We show that this solution is locally stable under noise, while under a sparsity assumption it remains unique under less demanding conditions. Sparsity in the context of unlabeled sensing leads to the problem of unlabeled compressed sensing, and a consequence of our general theory is the existence under mild conditions of a unique sparsest solution. On the algorithmic level, we solve unlabeled compressed sensing by an iterative algorithm validated by synthetic data experiments. Finally, under the unifying homomorphic sensing framework we connect unlabeled sensing to other important practical problems. Copyright © 2021 by the author(s)
会议录编者/会议主办者	Apple ; ByteDance ; et al. ; Facebook AI ; Invenia Labs ; MAYO Clinic, Center for Individualized Medicine
关键词	Iterative methods Machine learning Compressed-Sensing Condition Engineering applications Finite set General theory Linear maps Science and engineering Science applications Sensing problems Simple++
会议名称	38th International Conference on Machine Learning, ICML 2021
会议地点	Virtual, Online
会议日期	July 18, 2021 - July 24, 2021
URL	查看原文
收录类别	CPCI ; CPCI-S ; EI
语种	英语
出版者	ML Research Press
EI入藏号	20232414206131
EI主题词	Compressed sensing
EISSN	2640-3498
EI分类号	716.1 Information Theory and Signal Processing ; 723.4 Artificial Intelligence ; 921.6 Numerical Methods
原始文献类型	Conference article (CA)
文献类型	会议论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/133097
专题	信息科学与技术学院_硕士生信息科学与技术学院_PI研究组_Manolis Tsakiris组信息科学与技术学院_本科生
推荐引用方式 GB/T 7714	Liangzu Peng,Boshi Wang,Manolis Tsakiris. Homomorphic Sensing: Sparsity and Noise[C]//Apple, ByteDance, et al., Facebook AI, Invenia Labs, MAYO Clinic, Center for Individualized Medicine:ML Research Press,2021:8464-8475.