High-dimensional subset recovery in noise: Sparsified measurements without loss of statistical efficiency

@article{Omidiran2008HighdimensionalSR,
  title={High-dimensional subset recovery in noise: Sparsified measurements without loss of statistical efficiency},
  author={Dapo Omidiran and Martin J. Wainwright},
  journal={CoRR},
  year={2008},
  volume={abs/0805.3005}
}
We consider the problem of estimating the support of a vector β ∈ R based on observations contaminated by noise. A significant body of work has studied behavior of l1-relaxations when applied to measurement matrices drawn from standard dense ensembles (e.g., Gaussian, Bernoulli). In this paper, we analyze sparsified measurement ensembles, and consider the tradeoff between measurement sparsity, as measured by the fraction γ of non-zero entries, and the statistical efficiency, as measured by the… CONTINUE READING