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2013

Matrix Completion via Max-Norm Constrained Optimization

Cai, T. Tony, Zhou, Wen-Xin

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Matrix completion has been well studied under the uniform sampling model and the trace-norm regularized methods perform well both theoretically and numerically in such a setting.

However, the uniform sampling model is unrealistic for a range of applications and the standard trace-norm relaxation can behave very poorly when the underlying sampling scheme is non-uniform.
In this paper we propose and analyze a max-norm constrained empirical risk minimization method for noisy matrix completion under a general sampling model.
The optimal rate of convergence is established under the Frobenius norm loss in the context of approximately low-rank matrix reconstruction.

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