Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator

Note. The best result in each experiment is highlighted bold.The optimal solutions of many decision problems such as the Markowitz portfolio allocation and linear discriminant analysis depend on inverse covariance matrix a Gaussian random vector. In “Distributionally Robust Inverse Covariance Estimation: Wasserstein Shrinkage Estimator,” Nguyen, Kuhn, Mohajerin Esfahani propose distributionally robust estimator, obtained by robustifying maximum likelihood problem with ambiguity set. absence any prior structural information, estimation has an analytical solution that naturally interpreted nonlinear shrinkage estimator. Besides being invertible well conditioned, new estimator rotation equivariant preserves order eigenvalues sample matrix. If there are sparsity constraints, which typically encountered graphical models, can be solved using sequential quadratic approximation algorithm.