A method to estimate the graph structure for a large MRF model

Abstract

We propose a method to estimate the graph structure from data for a Markov random field (MRF) model. The method is valuable in many practical situations where the true topology is uncertain. First the similarities of the MRF variables are estimated by applying methods from information theory. Then, employing multidimensional scaling on the dissimilarity matrix obtained leads to a 2D topology estimate of the system. Finally, applying uniform thresholding on the node distances in the topology estimate gives the neighbourhood relations of the variables, hence defining the MRF graph estimate. Conditional independence properties of a MRF model are defined by the graph topology estimate thus enabling the estimation of the MRF model parameters e.g. through the pseudolikelihood estimation scheme. The proposed method is demonstrated by identifying MRF model for a telecommunications network, which can be used e.g. in analysing the effects of stochastic disturbances to the network state. © Springer-Verlag Berlin Heidelberg 2007.