Copula gaussian multi-scale graphical models - Zhang, Xu (2012)
Multi-scale graphical models have attracted a lot of interests in solving real world problems, especially for problems with large scale of data in applied fields of communication, image processing and bioinformatics. Its multi-scale structure renders it the capability to capture the long-range dependencies between variables that are far apart and simplify the analysis of the correlations in a large-scale dataset.In this work, we present a new type of multi-scale model named Copula Gaussian Multi-scale graphical model with Sparse In-scale conditional covariance (CSIM). The model is constructed as follows: This model first transforms non-Gaussian observed variables to Gaussian distributed variables using Gaussian copula. We then build a quad tree model by associating the transformed Gaussian variables with its finest scale, thus introducing hidden variables in the coarser scales naturally. Dependencies among the hidden variables in each coarser scale are captured using a sparse conditional covariance, successfully capturing the long-range dependencies with a few numbers of parameters.