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Weighted matrix completion from non-random, non-uniform sampling\n patterns

2019/10/30 by Simon Foucart, Deanna Needell, Foucart, Simon +7
Computer Science · Engineering · #Blind Source Separation Techniques #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST) #Target Tracking and Data Fusion in Sensor Networks

paper · pdf · doi:10.48550/arxiv.1910.13986

openalex publication_date 2019/10/30 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We study the matrix completion problem when the observation pattern is\ndeterministic and possibly non-uniform. We propose a simple and efficient\ndebiased projection scheme for recovery from noisy observations and analyze the\nerror under a suitable weighted metric. We introduce a simple function of the\nweight matrix and the sampling pattern that governs the accuracy of the\nrecovered matrix. We derive theoretical guarantees that upper bound the\nrecovery error and nearly matching lower bounds that showcase optimality in\nseveral regimes. Our numerical experiments demonstrate the computational\nefficiency and accuracy of our approach, and show that debiasing is essential\nwhen using non-uniform sampling patterns.\n

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