NIPS Proceedingsβ

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

Part of: Advances in Neural Information Processing Systems 26 (NIPS 2013)

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Authors

Conference Event Type: Poster

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-art Nuclear Norm and OptSpace methods.