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Concentration-Based Guarantees for Low-Rank Matrix Reconstruction

Concentration-Based Guarantees for Low-Rank Matrix Reconstruction

This video was recorded at 24th Annual Conference on Learning Theory (COLT), Budapest 2011. We consider the problem of approximately reconstructing a partially-observed, approximately low-rank matrix. This problem has received much attention lately, mostly using the trace-norm as a surrogate to the rank. Here we study low-rank matrix reconstruction using both the trace-norm, as well as the less-studied max-norm, and present reconstruction guarantees based on existing analysis on the Rademacher complexity of the unit balls of these norms. We show how these are superior in several ways to recently published guarantees based on specialized analysis.

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