| Research Abstract |
We have constructed the hyperparameter estimation algorithms for graphical models which can be treated analytically and have estimated the statistical performances of the algorithms analytically. The research results are published as two papers in Physical Review E, vol.65, no.1 and IEICE Transactions on Information and Systems, vol.ED-65, no.3. We have introduced quantized line fields to compound Gauss-Markov random field model and have succeeded in constructing a useful algorithm for grey-level image restoration. The compound Gauss-Markov random field model is one of familiar graphical models which are powerful for image restoration and dedge etection. The compound Gauss-Markov random field model with quantized line fields can take states expressed as a superposition of edge state and no edge state. The algorithm for image restorations is constructed by using the mean-field approximation. The research results have been published as two papers in IEICE Transactions on Information and Systems, vol.J64-D-II, no.4, 2001 and Journal of Physics A, vol.35, no.37, 2002. We have reformulated a generalized belief propagation for probabilistic inference in artificial intelligence by combining a cluster variation method and a linear response theory, which are ones of familiar techniques in the statistical mechanics and applied the framework to some practical probabilistic inferences in artificial intelligence.The research results have been reported in the SICE Symposium on Systems and Information (RIKEN, Yokohama Genome Science Center, Japan, November 2002) and NIPS*2002 Workshop on Propagation Algorithm on Graphs with Cycles: Theory and Applications (Whistler, Canada, December 2002), and will appear as a paper in IEICE Transactions on Information and Systems, voi.E86-D, no.7 on July 2003.
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