Numerical recipes: the art of scientific computing
Numerical recipes: the art of scientific computing
Elements of information theory
Elements of information theory
Information Theory, Inference & Learning Algorithms
Information Theory, Inference & Learning Algorithms
Gaussian Markov Random Fields: Theory And Applications (Monographs on Statistics and Applied Probability)
Statistical Model Describing Networked Systems Phenomena
ISCC '06 Proceedings of the 11th IEEE Symposium on Computers and Communications
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction (Stochastic Modelling and Applied Probability)
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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.