102 lines
3.4 KiB
Markdown
102 lines
3.4 KiB
Markdown
DART booster
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============
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[XGBoost](https://github.com/dmlc/xgboost)) mostly combines a huge number of regression trees with small learning rate.
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In this situation, trees added early are significance and trees added late are unimportant.
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Rasmi et.al proposed a new method to add dropout techniques from deep neural nets community to boosted trees, and reported better results in some situations.
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This is a instruction of new tree booster `dart`.
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Original paper
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--------------
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Rashmi Korlakai Vinayak, Ran Gilad-Bachrach. "DART: Dropouts meet Multiple Additive Regression Trees." [JMLR](http://www.jmlr.org/proceedings/papers/v38/korlakaivinayak15.pdf)
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Features
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--------
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- Drop trees in order to solve the over-fitting.
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- Trivial trees (to correct trivial errors) may be prevented.
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Because the randomness introduced in the training, expect the following few difference.
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- Training can be slower than `gbtree` because the random dropout prevents usage of prediction buffer.
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- The early stop might not be stable, due to the randomness.
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How it works
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------------
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- In ``$ m $``th training round, suppose ``$ k $`` trees are selected drop.
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- Let ``$ D = \sum_{i \in \mathbf{K}} F_i $`` be leaf scores of dropped trees and ``$ F_m = \eta \tilde{F}_m $`` be leaf scores of a new tree.
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- The objective function is following:
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```math
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\mathrm{Obj}
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= \sum_{j=1}^n L \left( y_j, \hat{y}_j^{m-1} - D_j + \tilde{F}_m \right)
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+ \Omega \left( \tilde{F}_m \right).
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```
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- ``$ D $`` and ``$ F_m $`` are overshooting, so using scale factor
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```math
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\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) .
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```
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Parameters
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----------
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### booster
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* `dart`
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This booster inherits `gbtree`, so `dart` has also `eta`, `gamma`, `max_depth` and so on.
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Additional parameters are noted below.
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### sample_type
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type of sampling algorithm.
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* `uniform`: (default) dropped trees are selected uniformly.
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* `weighted`: dropped trees are selected in proportion to weight.
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### normalize_type
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type of normalization algorithm.
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* `tree`: (default) New trees have the same weight of each of dropped trees.
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```math
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a \left( \sum_{i \in \mathbf{K}} F_i + \frac{1}{k} F_m \right)
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&= a \left( \sum_{i \in \mathbf{K}} F_i + \frac{\eta}{k} \tilde{F}_m \right) \\
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&\sim a \left( 1 + \frac{\eta}{k} \right) D \\
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&= a \frac{k + \eta}{k} D = D , \\
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&\quad a = \frac{k}{k + \eta} .
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```
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* `forest`: New trees have the same weight of sum of dropped trees (forest).
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```math
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a \left( \sum_{i \in \mathbf{K}} F_i + F_m \right)
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&= a \left( \sum_{i \in \mathbf{K}} F_i + \eta \tilde{F}_m \right) \\
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&\sim a \left( 1 + \eta \right) D \\
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&= a (1 + \eta) D = D , \\
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&\quad a = \frac{1}{1 + \eta} .
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```
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### rate_drop
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dropout rate.
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- range: [0.0, 1.0]
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### skip_drop
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probability of skipping dropout.
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- If a dropout is skipped, new trees are added in the same manner as gbtree.
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- range: [0.0, 1.0]
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Sample Script
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-------------
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```python
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import xgboost as xgb
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# read in data
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dtrain = xgb.DMatrix('demo/data/agaricus.txt.train')
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dtest = xgb.DMatrix('demo/data/agaricus.txt.test')
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# specify parameters via map
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param = {'booster': 'dart',
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'max_depth': 5, 'learning_rate': 0.1,
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'objective': 'binary:logistic', 'silent': True,
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'sample_type': 'uniform',
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'normalize_type': 'tree',
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'rate_drop': 0.1,
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'skip_drop': 0.5}
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num_round = 50
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bst = xgb.train(param, dtrain, num_round)
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# make prediction
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# ntree_limit must not be 0
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preds = bst.predict(dtest, ntree_limit=num_round)
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```
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