概率图模型 ——（6）团树传播算法

一、变量消元与团树的关系

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723135031465.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723135955604.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723140812929.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723141207403.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

算法流程：

利用变量消元构造团树，团树节点势函数初始化；
选取变量 X 所在的节点为根节点；
计算叶子节点到根节点的消息；
![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723143108928.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)
根节点的势函数乘以来自邻节点的消息；
计算变量 X 所在节点的边缘概率。

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723143217931.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)
![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723143228975.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723143506574.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723143519133.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)
![在这里插入图片描述]( https://img-blog.csdnimg.cn/2020072314354030.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723143609918.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)