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fix display problems (#33)
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* fix display problems
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youngfish42 authored Jul 9, 2023
1 parent 9830a08 commit 0533480
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2 changes: 1 addition & 1 deletion docs/chapter3/chapter3.md
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Expand Up @@ -45,7 +45,7 @@ $$

函数空间$\mathcal F$关于$\mathcal Z$在分布$\mathcal D$上的Rademacher复杂度为:
$$
\Re_{\mathcal Z}(\mathcal F)=E_{Z\subset\mathcal Z:|Z|=m}[\hat\Re_{\mathcal Z}(\mathcal F)]=E_{Z\subset\mathcal Z:|Z|=m}[E_{\sigma}[\underset{f\in\mathcal F}{sup}\frac{1}{m}\sideset{}{_{i=1}^m}\sum\sigma_i f(z_i)]]
\Re_{\mathcal Z}(\mathcal F)=E_{Z\subset\mathcal Z:|Z|=m}[\hat\Re_{\mathcal Z}(\mathcal F)]=E_{Z\subset\mathcal Z:|Z|=m}[E_{\sigma}[\underset{f\in\mathcal F}{sup}\frac{1}{m} \sum_{i=1}^m \sigma_i f(z_i)]]
$$
这里$\sigma_i$是${-1,+1}$上服从均匀分布的随机变量。如果将$\sigma_i$改为其他分布,会得到一些别的复杂度定义。

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10 changes: 6 additions & 4 deletions docs/chapter6/chapter6.md
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Expand Up @@ -56,17 +56,19 @@ P122,介绍一种将样本空间划分成多个互不相容的区域,然后

一种典型的方案就是我们熟悉的决策树模型:

<center><img src="imgs/1.png" width= "800"/></center>
![](imgs/1.png)

每当构造出一个决策树的节点时,就等同于在样本空间上做出了一次划分。这一洞察方式同样可解释剪枝操作,例如剪枝前的样本空间为:

<center><img src="imgs/2.png" width= "400"/></center>

每当构造出一个决策树的节点时,就等同于在样本空间上做出了一次划分。这一洞察方式同样可解释剪枝操作,例如剪枝前的样本空间为:

![](imgs/2.png)

而剪枝之后则为:

<center><img src="imgs/3.png" width= "400"/></center>
![](imgs/3.png)



此即所谓的划分机制。

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