A max-norm constrained minimization approach to 1-bit matrix completion

@article{Cai2013AMC,
  title={A max-norm constrained minimization approach to 1-bit matrix completion},
  author={Tony Cai and Wen-Xin Zhou},
  journal={Journal of Machine Learning Research},
  year={2013},
  volume={14},
  pages={3619-3647}
}
We consider in this paper the problem of noisy 1-bit matrix completion under a general non-uniform sampling distribution using the max-norm as a convex relaxation for the rank. A max-norm constrained maximum likelihood estimate is introduced and studied. The rate of convergence for the estimate is obtained. Information-theoretical methods are used to establish a minimax lower bound under the general sampling model. The minimax upper and lower bounds together yield the optimal rate of… CONTINUE READING
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