Estimation of (near) low-rank matrices with noise and high-dimensional scaling

@inproceedings{Negahban2010EstimationO,
  title={Estimation of (near) low-rank matrices with noise and high-dimensional scaling},
  author={Sahand N. Negahban and M. Wainwright},
  booktitle={ICML},
  year={2010}
}
We study an instance of high-dimensional statistical inference in which the goal is to use N noisy observations to estimate a matrix Θ+ ∈ ℝk×p that is assumed to be either exactly low rank, or "near" low-rank, meaning that it can be well-approximated by a matrix with low rank. We consider an M-estimator based on regularization by the trace or nuclear norm over matrices, and analyze its performance under high-dimensional scaling. We provide non-asymptotic bounds on the Frobenius norm error that… Expand
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