English

Obtaining error-minimizing estimates and universal entry-wise error bounds for low-rank matrix completion

Machine Learning 2013-04-02 v2 Algebraic Geometry Combinatorics

Abstract

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-are Nuclear Norm and OptSpace methods.

Keywords

Cite

@article{arxiv.1302.5337,
  title  = {Obtaining error-minimizing estimates and universal entry-wise error bounds for low-rank matrix completion},
  author = {Franz J. Király and Louis Theran},
  journal= {arXiv preprint arXiv:1302.5337},
  year   = {2013}
}

Comments

14 pages with appendix, 2 figures, v2 adds larger experiments and smoother exposition

R2 v1 2026-06-21T23:30:15.688Z