An efficiency upper bound for inverse covariance estimation

@article{Eldan2015AnEU,
  title={An efficiency upper bound for inverse covariance estimation},
  author={Ronen Eldan},
  journal={Israel Journal of Mathematics},
  year={2015},
  volume={207},
  pages={1-9}
}
  • Ronen Eldan
  • Published 3 December 2011
  • Mathematics
  • Israel Journal of Mathematics
We derive a quantitative upper bound for the efficiency of estimating entries in the inverse covariance matrix of a high dimensional distribution. We show that in order to approximate an off-diagonal entry of the density matrix of a d-dimensional Gaussian random vector, one needs at least a number of samples proportional to d. Furthermore, we show that with n ≪ d samples, the hypothesis that two given coordinates are fully correlated, when all other coordinates are conditioned to be zero… 
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