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arXiv · 1112.0669

An efficiency upper bound for inverse covariance estimation

Ronen Eldan
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Abstract

We derive an 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 $n \ll d$ samples, the hypothesis that two given coordinates are fully correlated, when all other coordinates are conditioned to be zero, cannot be told apart from the hypothesis that the two are uncorrelated.

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Ronen Eldan. 2013-02-11. An efficiency upper bound for inverse covariance estimation. https://doi.org/10.1007/s11856-015-1169-5

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