DART booster

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.

Original paper

Rashmi Korlakai Vinayak, Ran Gilad-Bachrach. “DART: Dropouts meet Multiple Additive Regression Trees.” [PMLR, arXiv].

Features

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.

How it works

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

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

Parameters

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]

Sample Script

import xgboost as xgb
# read in data
dtrain = xgb.DMatrix('demo/data/agaricus.txt.train?format=libsvm')
dtest = xgb.DMatrix('demo/data/agaricus.txt.test?format=libsvm')
# 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)