Author Topic Model[ATM理解及公式推导]

原文地址：http://blog.csdn.net/qy20115549/article/details/54407099

**由于初学LDA，内容可能有不到之处，欢迎交流。**

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](http://img.blog.csdn.net/20170113111714828?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvcXkyMDExNTU0OQ==/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/SouthEast)

![这里写图片描述](http://img.blog.csdn.net/20170113111254041?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvcXkyMDExNTU0OQ==/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/SouthEast)

![这里写图片描述](http://img.blog.csdn.net/20170113111459177?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvcXkyMDExNTU0OQ==/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/SouthEast)

#Modeling authors with words

![这里写图片描述](http://img.blog.csdn.net/20170113111628436?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvcXkyMDExNTU0OQ==/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/SouthEast)

![这里写图片描述](http://img.blog.csdn.net/20170113111741016?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvcXkyMDExNTU0OQ==/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/SouthEast)

#The author-topic model
![这里写图片描述](http://img.blog.csdn.net/20170113111826002?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvcXkyMDExNTU0OQ==/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/SouthEast)

![这里写图片描述](http://img.blog.csdn.net/20170113111900163?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvcXkyMDExNTU0OQ==/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/SouthEast)

#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](http://img.blog.csdn.net/20170113112359823?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvcXkyMDExNTU0OQ==/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/SouthEast)

##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](http://img.blog.csdn.net/20170113112910376?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvcXkyMDExNTU0OQ==/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/SouthEast)

![这里写图片描述](http://img.blog.csdn.net/20170113112706791?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvcXkyMDExNTU0OQ==/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/SouthEast)

![这里写图片描述](http://img.blog.csdn.net/20170113112759515?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvcXkyMDExNTU0OQ==/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/SouthEast)

![这里写图片描述](http://img.blog.csdn.net/20170113112835933?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvcXkyMDExNTU0OQ==/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/SouthEast)

##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](http://img.blog.csdn.net/20170113113026215?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvcXkyMDExNTU0OQ==/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/SouthEast)

![这里写图片描述](http://img.blog.csdn.net/20170113113208927?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvcXkyMDExNTU0OQ==/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/SouthEast)

![这里写图片描述](http://img.blog.csdn.net/20170113113240006?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQvcXkyMDExNTU0OQ==/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/SouthEast)

Author Topic Model[ATM理解及公式推导]

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