Seminar on Markov Random Fields – Niels Bohr Institute - University of Copenhagen

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Seminar on Markov Random Fields

Talk by Håkon Tjelmeland
The famous Ising model from physics are also frequently used in statistics to model spatial heterogeneity of discrete variables. The Ising model have pairwise interactions between the values in neighbouring nodes in a lattice. In this presentation we argue that pairwise interaction is insufficient to model many scenes of interest in statistics. Therefore we consider the more general model class of Markov random fields (MRFs). The Ising model is an MRF, but an MRF is more general in that it may also include higher-order interactions. Like the Ising model, also MRFs include a computationally intractable normalizing constant or partition function, and this limits the type of inference one can do for MRFs.

This presentation is focusing on two aspects of higher-order interaction binary MRFs. The first is an approximation of the normalizing constant, and a corresponding approximation of the MRF. Using such an approximate model in stead of the MRF itself statistical inference can be performed more easily. The second focus is on how to estimate or fit a higher-order interaction MRF to an observed scene. To estimate or fit a model includes both to decide what interactions to include in the model and to estimate the model parameters of the chosen parametric model.