Error-Minimizing Estimates and Universal Entry-Wise Error Bounds for Low-Rank Matrix Completion

Authors: Franz J. Király and Louis Theran
Proc. of: Advances in Neural Information Processing Systems NIPS’13, 2013.
Full text: arXiv URL

We propose a general framework for reconstructing and denoising single entries of incomplete and noisy entries. We describe: effective algorithms for deciding if and entry can be reconstructed and, if so, for reconstructing and denoising it; and a priori bounds on the error of each entry, individually. In the noiseless case our algorithm is exact. For rank-one matrices, the new algorithm is fast, admits a highly-parallel implementation, and produces an error minimizing estimate that is qualitatively close to our theoretical and the state-of-the-art Nuclear Norm and OptSpace methods.