# 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


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://windmising.gitbook.io/lihang-tongjixuexifangfa/em/5.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.