概率图模型 ——（5）变量消元法求边缘概率

一、推理问题的分类
二、变量消元法
三、小结

一、推理问题的分类

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723105124605.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

二、变量消元法

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723105612446.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/2020072311071581.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

2.1 示例1

![在这里插入图片描述]( https://img-blog.csdnimg.cn/2020072310565015.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/20200723105704519.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/20200723105714931.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/20200723105723732.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

2.2 示例2

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723105805675.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/20200723110259928.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/20200723110312291.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/20200723110343771.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/20200723110410585.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/20200723110421825.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/20200723110452296.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/20200723110502934.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/20200723110516280.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

变量消元的顺序并不是固定的，可以任意改变
![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723110617848.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

2.3 变量消元法时间复杂度分析

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723110807146.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

2.4 导出图

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723110845844.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/20200723110857984.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

2.5 变量消元法消元顺序

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723110941991.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)

三、小结

![在这里插入图片描述]( https://img-blog.csdnimg.cn/20200723111036317.png?x-oss-process=image/watermark ,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzM0MjEzMjYw,size_16,color_FFFFFF,t_70)