Multiscale Gaussian Graphical Models and Algorithms for Large-Scale Inference

We propose a class of multiscale graphical models and algorithms to estimate means and approximate error variances of large-scale Gaussian processes efficiently. Based on emerging techniques for inference on Gaussian graphical models with cycles, we extend traditional multiscale tree models to pyramidal graphs, which incorporate both inter- and intra- scale interactions. In the spirit of multipole algorithms, we develop efficient inference methods in which variables far-apart communicate through coarser resolutions and nearby variables interact at finer resolutions. In addition, we propose methods to update the estimates rapidly when measurements are added or new knowledge of a local region is provided.