A Heuristic for Completing Covariance And Correlation Matrices

Abstract

In practical applications, and especially in high dimensional models, it is common that not all covariances are known due to, for example, data limitations. In such situations, the covariance matrix must be completed in order to use the statisti-cal or stochastic model at hand. The already specified covariances generically imply a dependence between variables between which the covariance is unspecified. A criterion that can then be used to complete the covariance matrix is to introduce as little extra dependence between variables as possible which is equivalent with entropy maximization. Such completion problems can be solved with global optimization al-gorithms which unfortunately are slow for large matrices. And thus, this makes global optimization less suitable for applications in which the computation time is important. Another difficulty is that the initially specified covariances can be inconsistent in the sense that no valid completion exists. In this paper, we present a heuristic for complet-ing partially specified covariance (and correlation) matrices that is: fast (also for large matrices), tries to introduce as little extra dependence between variables as possible and also corrects for inconsistencies in the initially specified covariances. Finally, we present error measures for the performance of the heuristic.