Low-Rank Variance Estimation in Large-Scale Gmrf Models

We consider the problem of variance estimation in large-scale Gauss-Markov random field (GMRF) models. While approximate mean estimates can be obtained efficiently for sparse GMRFs of very large size, computing the variances is a challenging problem. We propose a simple rank-reduced method which exploits the graph structure and the correlation length in the model to compute approximate variances with linear complexity in the number of nodes. The method has a separation length parameter trading off complexity versus estimation accuracy. For models with bounded correlation length, we efficiently compute provably accurate variance estimates