> For the complete documentation index, see [llms.txt](https://windmising.gitbook.io/lihang-tongjixuexifangfa/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://windmising.gitbook.io/lihang-tongjixuexifangfa/em/5.md).

# Q函数推导

使用EM算法最关键的是写出Q函数。\
写出Q函数的第一步是找出隐变量。

高斯混合模型的EM算法，有几个地方不懂：\
1\. 9.27的$$\gamma$$定义的有点啰嗦，这样定义是否可以？\
$$\gamma \in \[1,K]$$\
$$\gamma\_j$$表示第j个数据所使用的模型？\
2\. 9.11公式：

$$
Q(\theta, \theta^{(i)}) = E\_Z\[\log P(Y,Z|\theta)|Y, \theta^{(i)}]
$$

9.17公式：

$$
Q(\theta, \theta^{(i)}) = \sum\_ZP(Z|Y,\theta^{(i)})\log P(Y, Z|\theta)
$$

9.28求得的$$\log P(y,\gamma|\theta)$$相当于Q函数中的$$\log P(Y, Z|\theta)$$了。\
接下来求Q函数时为什么用上面的公式不用下面的？\
3\. 9.28算期望怎么算的？看不懂


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