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

我们已经研究了一些数学结构的计算模型，通过使用马尔可夫随机场和循环的信念传播的概率ad-hoc网络系统的设计。虽然马尔可夫随机场是有用的概率图像处理系统，ad-hoc网络系统中构建的随机图，其中有大量的度在每个节点。从这一观点出发，我们利用循环信念传播建立了这类随机图的计算模型，并发现在这类计算模型中，某些统计量作为超参数的函数存在若干奇异点.此外，我们已经成功地将我们的设计策略应用于城市交通中各条道路的交通密度预测系统。这也是我们在本研究项目的应用中所没有预料到的结果。

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.