# 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} }

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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