Extreme Compressive Sampling for Covariance Estimation

@article{Azizyan2018ExtremeCS,
  title={Extreme Compressive Sampling for Covariance Estimation},
  author={Martin Azizyan and A. Krishnamurthy and Aarti Singh},
  journal={IEEE Transactions on Information Theory},
  year={2018},
  volume={64},
  pages={7613-7635}
}
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A distribution-free analysis shows that by observing just a single linear measurement of each vector, one can consistently estimate the covariance matrix, in both infinity and spectral norm, and this analysis leads to precise rates of convergence in both norms… Expand
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