XGBoost mostly combines a huge number of regression trees with a small learning rate. In this situation, trees added early are significant and trees added late are unimportant.

Vinayak and Gilad-Bachrach proposed a new method to add dropout techniques from the deep neural net community to boosted trees, and reported better results in some situations.

This is a instruction of new tree booster `dart`

.

Rashmi Korlakai Vinayak, Ran Gilad-Bachrach. “DART: Dropouts meet Multiple Additive Regression Trees.” JMLR.

Drop trees in order to solve the over-fitting.

Trivial trees (to correct trivial errors) may be prevented.

Because of the randomness introduced in the training, expect the following few differences:

Training can be slower than

`gbtree`

because the random dropout prevents usage of the prediction buffer.The early stop might not be stable, due to the randomness.

In \(m\)-th training round, suppose \(k\) trees are selected to be dropped.

Let \(D = \sum_{i \in \mathbf{K}} F_i\) be the leaf scores of dropped trees and \(F_m = \eta \tilde{F}_m\) be the leaf scores of a new tree.

The objective function is as follows:

\[\mathrm{Obj}
= \sum_{j=1}^n L \left( y_j, \hat{y}_j^{m-1} - D_j + \tilde{F}_m \right)
+ \Omega \left( \tilde{F}_m \right).\]

\(D\) and \(F_m\) are overshooting, so using scale factor

\[\hat{y}_j^m = \sum_{i \not\in \mathbf{K}} F_i + a \left( \sum_{i \in \mathbf{K}} F_i + b F_m \right) .\]

The booster `dart`

inherits `gbtree`

booster, so it supports all parameters that `gbtree`

does, such as `eta`

, `gamma`

, `max_depth`

etc.

Additional parameters are noted below:

`sample_type`

: type of sampling algorithm.`uniform`

: (default) dropped trees are selected uniformly.`weighted`

: dropped trees are selected in proportion to weight.

`normalize_type`

: type of normalization algorithm.`tree`

: (default) New trees have the same weight of each of dropped trees.

\[\begin{split}a \left( \sum_{i \in \mathbf{K}} F_i + \frac{1}{k} F_m \right) &= a \left( \sum_{i \in \mathbf{K}} F_i + \frac{\eta}{k} \tilde{F}_m \right) \\ &\sim a \left( 1 + \frac{\eta}{k} \right) D \\ &= a \frac{k + \eta}{k} D = D , \\ &\quad a = \frac{k}{k + \eta}\end{split}\]`forest`

: New trees have the same weight of sum of dropped trees (forest).

\[\begin{split}a \left( \sum_{i \in \mathbf{K}} F_i + F_m \right) &= a \left( \sum_{i \in \mathbf{K}} F_i + \eta \tilde{F}_m \right) \\ &\sim a \left( 1 + \eta \right) D \\ &= a (1 + \eta) D = D , \\ &\quad a = \frac{1}{1 + \eta} .\end{split}\]`rate_drop`

: dropout rate.range: [0.0, 1.0]

`skip_drop`

: probability of skipping dropout.If a dropout is skipped, new trees are added in the same manner as gbtree.

range: [0.0, 1.0]

```
import xgboost as xgb
# read in data
dtrain = xgb.DMatrix('demo/data/agaricus.txt.train')
dtest = xgb.DMatrix('demo/data/agaricus.txt.test')
# specify parameters via map
param = {'booster': 'dart',
'max_depth': 5, 'learning_rate': 0.1,
'objective': 'binary:logistic',
'sample_type': 'uniform',
'normalize_type': 'tree',
'rate_drop': 0.1,
'skip_drop': 0.5}
num_round = 50
bst = xgb.train(param, dtrain, num_round)
preds = bst.predict(dtest)
```