Generation of fundamental design theory of Bayesian ad-hoc network systems based on Markov random fields

我们利用马尔可夫随机场和回路信任传播研究了概率自组织网络系统设计中计算模型的一些数学结构。虽然马尔可夫随机场对于概率图像处理系统是有用的，但自组织网络系统是根据每个节点具有大量度的随机图来构建的。在这一观点下，我们利用回路信任传播建立了这类随机图的高级计算模型，并在这类计算模型中发现了一些统计量的奇点的存在，这些奇点被认为是超参数的函数。此外，我们还成功地将我们的设计策略应用于城市交通中各个道路的交通密度预测系统中。这也是我们在应用本研究项目时无法预期的结果。

We have investigated some mathematical structures of computational models by using Markov random fields and loopy belief propagations for designs of probabilistic ad-hoc network systems. Although Markov random fields are useful for probabilistic image processing systems, ad-hoc network systems are constructed in terms of random graphs which have large number of degree at each node. In the stand point of view, we have formulated advanced computational models on such random graphs by using loopy belief propagations and have found the existence of several singular points in some statistical quantities, which are regarded as functions of hyperparameters, in such computational models. Moreover, we have succeeded in applying our design strategies to some prediction systems of the traffic density at each road in the city traffic. This is also our results which could not be expected at the application of the present research project.