Gibbs classifiers
B. A. Zalesky · Theory of Probability and Mathematical Statistics · 2005
New statistical classifiers for dependent observations with Gibbs prior distributions of the exponential or Gaussian type are presented.It is assumed that the observations are characterized by feature functions that assume values in finite sets of rational numbers.The distributions of observations are either Gibbs exponential or Gibbs Gaussian.Arbitrary neighborhoods on a completely connected graph are considered instead of local neighborhoods of the nearest observation.The models studied in this paper can be used for some problems of the classification of random fields, in statistical physics, and for image processing.A method of finding an optimal Bayes decision rule is described.The method is based on the reduction of the problem to the evaluation of the minimal cut of an appropriate graph.The method can be used for the fast evaluation of optimal Bayes decision rules for large samples.