Presentation + Paper
24 August 2017 De-biasing low-rank projection for matrix completion
Simon Foucart, Deanna Needell, Yaniv Plan, Mary Wootters
Author Affiliations +
Abstract
We study matrix completion with non-uniform, deterministic sampling patterns. We introduce a computable parameter, which is a function of the sampling pattern, and show that if this parameter is small, then we may recover missing entries of the matrix, with appropriate weights. We theoretically analyze a simple and well-known recovery method, which simply projects the (zero-padded) subsampled matrix onto the set of low-rank matrices. We show that under non-uniform deterministic sampling, this method yields a biased solution, and we propose an algorithm to de-bias it. Numerical simulations demonstrate that de-biasing significantly improves the estimate. However, when the observations are noisy, the error of this method can be sub-optimal when the sampling is highly non-uniform. To remedy this, we suggest an alternative which is based on projection onto the max-norm ball whose robustness to noise tolerates arbitrarily non-uniform sampling. Finally, we analyze convex optimization in this framework.
Conference Presentation
© (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Simon Foucart, Deanna Needell, Yaniv Plan, and Mary Wootters "De-biasing low-rank projection for matrix completion", Proc. SPIE 10394, Wavelets and Sparsity XVII, 1039417 (24 August 2017); https://doi.org/10.1117/12.2275004
Lens.org Logo
CITATIONS
Cited by 6 scholarly publications.
Advertisement
Advertisement
RIGHTS & PERMISSIONS
Get copyright permission  Get copyright permission on Copyright Marketplace
KEYWORDS
Statistical analysis

Back to Top