Verification Under Increasing Dimensionality

Verification decisions are often based on second order statistics estimated from a set of samples. Ongoing growth of computational resources allows for considering more and more features, increasing the dimensionality of the samples. If the dimensionality is of the same order as the number of samples used in the estimation or even higher, then the accuracy of the estimate decreases significantly. In particular, the eigenvalues of the covariance matrix are estimated with a bias and the estimate of the eigenvectors differ considerably from the real eigenvectors. We show how a classical approach of verification in high dimensions is severely affected by these problems, and we show how bias correction methods can reduce these problems.