Probabilistic data mining theory using item response theory based on Markov random field

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An item response theory (IRT)is a recent statistical test theory which has been mainly developed in social science and psychology. In conventional models of IRT, each item has been statistically independent of each other. In this research program, I have proposed a new probabilistic model of an IRT including correlations among items, and have proposed approximate techniques and machine learning algorithms for the proposed model. Since the model is mathematically equivalent to Boltzmann machines which are well known in the area of neural networks and the area of machine learning, the proposed methods can be applied to not only the IRT but also applications in those areas.