Application of Tunneling Effect in Quantized Probabilistic Model to Intelligent Information Processing

构造了可解析处理的图形模型的超参数估计算法，并对算法的统计性能进行了解析估计。该研究结果以两篇论文的形式发表在《物理评论E》第65卷第5期。《信息与系统学报》，第65卷，第3期。我们在复合高斯-马尔科夫随机场模型中引入了量化的线场，并成功地构建了一种有用的灰度图像恢复算法。复合高斯-马尔可夫随机场模型是一种常见的图形模型，具有很强的图像恢复和边缘检测功能。具有量子化线场的复合高斯-马尔可夫随机场模型可以将状态表示为边缘状态和无边缘状态的叠加。利用平均场近似构造了图像恢复算法。研究结果已作为两篇论文发表在IEICE Transactions on Information and Systems， vol.J64-D-II, no. 5。物理学报A卷，第35期，2001。2002年37岁。结合统计力学中常见的聚类变分法和线性响应理论，重新构造了人工智能概率推理的广义信念传播框架，并将其应用于实际的人工智能概率推理中。研究结果已在2002年11月召开的SICE系统与信息学术研讨会（RIKEN, Yokohama Genome Science Center, Japan， 11月）和2002年NIPS*循环图的传播算法研讨会（Whistler, Canada， 2002年12月）上发表，并将作为论文发表在IEICE Transactions on Information and Systems， voi。E86-D,不。2003年7月7日。

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.