A low rank matrix X has been contaminated by uniformly distributed noise, missing values, outliers and corrupt entries. Reconstruction of X from the singular values and singular vectors of the contaminated matrix Y is a key problem in machine learning, computer vision and data science. In this paper, we show that common contamination models (including arbitrary combinations of uniform noise, missing values, outliers and corrupt entries) can be described efficiently using a single framework. We develop an asymptotically optimal algorithm that estimates X by manipulation of the singular values of Y, which applies to any of the contamination models considered. Finally, we find an explicit signal-to-noise cutoff, below which estimation of X from the singular value decomposition of Y must fail, in a well-defined sense.
|Number of pages
|Advances in Neural Information Processing Systems
|Published - 2017
|31st Annual Conference on Neural Information Processing Systems, NIPS 2017 - Long Beach, United States
Duration: 4 Dec 2017 → 9 Dec 2017
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© 2017 Neural information processing systems foundation. All rights reserved.