Hendrik/xgboost
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

refine model doc

Browse Source
This commit is contained in:
hetong007 2015-08-23 17:04:08 -07:00
parent cc3c98d9b7
commit 7294ac4fc9
1 changed files with 2 additions and 2 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

4
doc/model.md
View File

@ -63,7 +63,7 @@ Now we are predicting with two trees, by predict on each tree individually and t
\hat{y}_i = \sum_{k=1}^K f_k(x_i), f_k \in F
```
where ``$ f $`` is a function in the functional space ``$ F $``, and ``$ F $`` is the set of all possible CARTs. Therefore our objective to optimize can be written as
where ``$ K $`` is the number of trees, ``$ f $`` is a function in the functional space ``$ F $``, and ``$ F $`` is the set of all possible CARTs. Therefore our objective to optimize can be written as
```math
obj(\Theta) = \sum_i^n l(y_i, \hat{y}_i) + \sum_{k=1}^K \Omega(f_k)
@ -137,7 +137,7 @@ It is possible to define other form of regularization terms, but this one works
Now we have the objective value with the ``$ t $``-th tree added:
```math
Obj^{(t)} &\approx \sum_{i=1}^n [g_i w_q(x_i) + \frac{1}{2} h_i w_{q(x_i)}^2] + \gamma T + \frac{1}{2}\lambda \sum_{j=1}^T w_j^2\\
Obj^{(t)} &\approx \sum_{i=1}^n [g_i w_{q(x_i)} + \frac{1}{2} h_i w_{q(x_i)}^2] + \gamma T + \frac{1}{2}\lambda \sum_{j=1}^T w_j^2\\
&= \sum^T_{j=1} [(\sum_{i\in I_j} g_i) w_j + \frac{1}{2} (\sum_{i\in I_j} h_i + \lambda) w_j^2 ] + \gamma T
```