PGM：概率论基础知识

た入场券 2022-07-18 06:10 197阅读 0赞

http://[blog.csdn.net/pipisorry/article/details/52459847][blog.csdn.net_pipisorry_article_details_52459847]

概率图模型PGM：概率论基础知识

# 独立性与条件独立性 #

## 独立性 ##

![Center][]

![Center 1][]

## 条件独立性 ##

![Center 2][]

![Center 3][]

![Center 4][]

![Center 5][]

也就是![Center 6][]表示给定 c 的条件下 a 与 b 条件独立,等价于公式p(a | b, c) = p(a | c)

![Center 7][]

## 随机变量的独立性 ##

![Center 8][]

![Center 9][]

![Center 10][] 等价于 ![Center 11][]

### 条件独立性的性质    ###

![Center 12][]

这里是前面的独立性可以导出后面的独立性，而不是等价于后面的独立性。

![Center 13][]

![Center 14][]

### 条件独立的证明 ###

如分解性质可以通过积分w证明；其实画个概率图来更容易分析了。

## 独立性性质的利用 ##

![Center 15][]

![Center 16][]

![Center 17][]

[皮皮blog][blog]

# 查询一个分布 #

## 概率查询 ##

![Center 18][]

## 最大后验MAP查询 ##

![Center 19][]

![Center 20][]

\[[文本分析的参数估计方法 ][Link 1]最大后验估计MAP\]

### 边缘最大后验概率查询 ###

...

[皮皮blog][blog]

# 连续空间 #

概率密度函数

联合密度函数

条件密度函数

[皮皮blog][blog]

\[[概率论：均值、方差与协方差矩阵 ][Link 2]\]

from:  [http://blog.csdn.net/pipisorry/article/details/52459847][blog.csdn.net_pipisorry_article_details_52459847]

ref:

[blog.csdn.net_pipisorry_article_details_52459847]: http://blog.csdn.net/pipisorry/article/details/52459847
[Center]: /images/20220717/beff10b3f24b476e81b44b5468025d75.png
[Center 1]: /images/20220717/84b81c6622ff41b189debf3857a523b9.png
[Center 2]: /images/20220717/8f3c0e3948024d4e953775ac51a2fcc4.png
[Center 3]: /images/20220717/2ea9200ec496403180661113f9e5d3e5.png
[Center 4]: /images/20220717/e3b27f92d5394248bbc2ed2342baa9c9.png
[Center 5]: /images/20220717/987d51174b314b6ca2296719542eefd9.png
[Center 6]: /images/20220717/87df45381b4a4d17b25a74230e099c1a.png
[Center 7]: /images/20220717/760ca6135f3b4006a0f499460b43dfdd.png
[Center 8]: /images/20220717/977e4e6189c443f18569bded4b0b86f2.png
[Center 9]: /images/20220717/bab646b28ef54d2e86fc92b73267f748.png
[Center 10]: https://img-blog.csdn.net/20160907161804374?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQv/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/Center
[Center 11]: /images/20220717/4cd6eb529ee8423694d7b309eaaec0c7.png
[Center 12]: /images/20220717/72781b2e9d0940059723410e4d44ac24.png
[Center 13]: /images/20220717/c2ce8a7fc8614b15bf7dabe429b6f097.png
[Center 14]: /images/20220717/eedd0fa07f264c64a81e534a30bbfb41.png
[Center 15]: /images/20220717/1a489152d56b45a380dfa0ba54693efe.png
[Center 16]: /images/20220717/7a719c9ed46047a0befa9a8464d76d15.png
[Center 17]: /images/20220717/ebe50faee11b4d40a33bd93475687b6e.png
[blog]: http://blog.csdn.net/pipisorry
[Center 18]: /images/20220717/55d3f06156bc4024ac585a32c453e6ae.png
[Center 19]: /images/20220717/f06f6b698f934d52a13d8742b03e7c98.png
[Center 20]: /images/20220717/7cdc20532fad44ddb3f611ce7dcee44d.png
[Link 1]: http://blog.csdn.net/pipisorry/article/details/51482120
[Link 2]: http://blog.csdn.net/pipisorry/article/details/48788671