Creative extensions of data mining theory by means of quantum-mechanical labeling

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General frameworks of statistical machine learning systems based on quantum-mechanical extended Markov random fields has been provided by using belief propagation methods. Some novel statistical model selection schemes by using quantum belief propagation methods have been proposed. As one of unexpected research results in our present project proposal, we have established new statistical learning frameworks for some statistical models with the first-order phase transitions in the stand point of constrained maximization ofentropies instead of conventional maximum likelihood estimations.