An efficiency upper bound for inverse covariance estimation

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.

7 Pages

References in corpus (3)

• Sparse permutation invariant covariance estimation
• Quantitative estimates of the convergence of the empirical covariance matrix in Log-concave Ensembles
• Moments of minors of Wishart matrices