Author Topic Model[ATM理解及公式推导]

矫情吗；* 2022-07-13 14:45 157阅读 0赞

*  参考论文
 *  Modeling documents with topics
 *  Modeling authors with words
 *  The author-topic model
 *  Gibbs sampling algorithms详细
    
     *  经典LDA模型目标分布及参数
     *  Author Model目标分布及参数
     *  Author-topic model目标分布及参数

**本文作者：合肥工业大学 管理学院 钱洋 email：1563178220@qq.com 由于初学LDA，内容可能有不到之处，欢迎交流。**  
该文的另一个地址：[http://www.datalearner.com/blog/1051484278666593][http_www.datalearner.com_blog_1051484278666593]  
由于敲公式太麻烦了，还是直接上图吧。

# 参考论文 #

本博客参考的论文是：

Rosen-Zvi M, Griffiths T, Steyvers M, et al. **The author-topic model for authors and documents**\[C\]//Proceedings of the 20th conference on Uncertainty in artificial intelligence. **AUAI** Press, 2004: 487-494.

# Modeling documents with topics #

![这里写图片描述][SouthEast]  
  
  
![这里写图片描述][SouthEast 1]  
  
  
![这里写图片描述][SouthEast 2]

# Modeling authors with words #

![这里写图片描述][SouthEast 3]  
  
  
![这里写图片描述][SouthEast 4]

# The author-topic model #

![这里写图片描述][SouthEast 5]  
  
  
![这里写图片描述][SouthEast 6]

# Gibbs sampling algorithms【详细】 #

**LDA的一些求解方法包括**：

A variety of algorithms have been used to estimate the parameters of topic models, from basice expectation maximization (**EM**; Hofmann, 1999), to approximate inference methods like **variational EM** (Blei et al.,2003), **expectation propagation** (Minka & Lafferty,2002), and **Gibbs sampling** (Griffiths & Steyvers,2004).

## 经典LDA模型目标分布及参数 ##

由于前面已经写过一篇想写的LDA推理的文章了，这里就不过多推理了。直接上图。

![这里写图片描述][SouthEast 7]

## Author Model目标分布及参数 ##

如下图所示，为其模型：

![这里写图片描述][SouthEast 8]  
  
  
![这里写图片描述][SouthEast 9]  
  
  
![这里写图片描述][SouthEast 10]  
  
  
![这里写图片描述][SouthEast 11]

## Author-topic model目标分布及参数 ##

如下图所示，为模型的概率图表示：

![这里写图片描述][SouthEast 12]  
  
  
![这里写图片描述][SouthEast 13]  
  
  
![这里写图片描述][SouthEast 14]

[http_www.datalearner.com_blog_1051484278666593]: http://www.datalearner.com/blog/1051484278666593
[SouthEast]: /images/20220713/5a5ece0d81284822b8b9ac96c9d3ac84.png
[SouthEast 1]: /images/20220713/e21f234973c340729c361e03768e5d85.png
[SouthEast 2]: /images/20220713/869eb24a44bf430ba5b9bffcf12584b5.png
[SouthEast 3]: /images/20220713/22eafa7041954e6e867904ec3b765da5.png
[SouthEast 4]: /images/20220713/84dc068a34214338971c43fb3a181caf.png
[SouthEast 5]: /images/20220713/32351ef14ae74769970318faaad5b198.png
[SouthEast 6]: /images/20220713/6baee7b1be3f4287822073b45cb372cf.png
[SouthEast 7]: /images/20220713/272c247f0d584c30bd86708200787055.png
[SouthEast 8]: /images/20220713/6228b55829dc4d0ab835f49c3151a3c2.png
[SouthEast 9]: /images/20220713/bd5174b3feba4d35943f5a74d327f56b.png
[SouthEast 10]: /images/20220713/b1a9f4d70ac74f96a92b0fc3eccb8900.png
[SouthEast 11]: /images/20220713/3d1fafa0fd034e52894c3d35876d11a4.png
[SouthEast 12]: /images/20220713/c7be2186bf5d48cfac051fc51b0d3d71.png
[SouthEast 13]: /images/20220713/90611f9009fa48a5b00f249695ac04b4.png
[SouthEast 14]: /images/20220713/497edf92c1cc42f181aa1882b7bc84fc.png