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Optimal Shrinkage of Singular Values Under Random Data Contamination
Danny Barash · Matan Gavish

Tue Dec 05 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #42

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.

Author Information

Danny Barash (The Hebrew University Of Jerusalem)
Matan Gavish (Hebrew University)