> 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/boostingtree/7.md).

# 回归问题提升树前向分步算法

**输入：**\
训练数据集T

**输出：** 提升树$$f\_M(x)$$

**过程：**\
1\. 令$$f\_0(x)=0$$\
2\. 对当前m计算残存差：

$$
r\_{mi} = y\_i - f\_{m-1}(x\_i), i = 1,2,\cdots,M
$$

1. 拟合残差$$r\_{mi}$$学习一个回归树，得到$$T(x;\Theta\_m)$$  
2. 更新$$f\_m(x) = f\_{m-1}(x) + T(x; \Theta\_m)$$
3. 重复2-4步M次，得到M个回归树  
4. 得到回归问题提升树：  

   $$
   f\_M(x) = \sum\_{m=1}^MT(x; \Theta\_m)
   $$