# DecisionTree.jl

Julia implementation of Decision Tree (CART) and Random Forest algorithms

Available via:

- CombineML.jl - a heterogeneous ensemble learning package
- MLJ.jl - a pure Julia machine learning framework
- ScikitLearn.jl - Julia implementation of the scikit-learn API

## Classification

- pre-pruning (max depth, min leaf size)
- post-pruning (pessimistic pruning)
- multi-threaded bagging (random forests)
- adaptive boosting (decision stumps)
- cross validation (n-fold)
- support for ordered features (encoded as
`Real`

s or`String`

s)

## Regression

- pre-pruning (max depth, min leaf size)
- multi-threaded bagging (random forests)
- cross validation (n-fold)
- support for numerical features

**Note that regression is implied if labels/targets are of type Array{Float}**

## Installation

You can install DecisionTree.jl using Julia's package manager

`Pkg.add("DecisionTree")`

## ScikitLearn.jl API

DecisionTree.jl supports the ScikitLearn.jl interface and algorithms (cross-validation, hyperparameter tuning, pipelines, etc.)

Available models: `DecisionTreeClassifier, DecisionTreeRegressor, RandomForestClassifier, RandomForestRegressor, AdaBoostStumpClassifier`

.
See each model's help (eg. `?DecisionTreeRegressor`

at the REPL) for more information

### Classification Example

Load DecisionTree package

`using DecisionTree`

Separate Fisher's Iris dataset features and labels

```
features, labels = load_data("iris") # also see "adult" and "digits" datasets
# the data loaded are of type Array{Any}
# cast them to concrete types for better performance
features = float.(features)
labels = string.(labels)
```

Pruned Tree Classifier

```
# train depth-truncated classifier
model = DecisionTreeClassifier(max_depth=2)
fit!(model, features, labels)
# pretty print of the tree, to a depth of 5 nodes (optional)
print_tree(model, 5)
# apply learned model
predict(model, [5.9,3.0,5.1,1.9])
# get the probability of each label
predict_proba(model, [5.9,3.0,5.1,1.9])
println(get_classes(model)) # returns the ordering of the columns in predict_proba's output
# run n-fold cross validation over 3 CV folds
# See ScikitLearn.jl for installation instructions
using ScikitLearn.CrossValidation: cross_val_score
accuracy = cross_val_score(model, features, labels, cv=3)
```

Also, have a look at these classification and regression notebooks.

## Native API

### Classification Example

Decision Tree Classifier

```
# train full-tree classifier
model = build_tree(labels, features)
# prune tree: merge leaves having >= 90% combined purity (default: 100%)
model = prune_tree(model, 0.9)
# pretty print of the tree, to a depth of 5 nodes (optional)
print_tree(model, 5)
# apply learned model
apply_tree(model, [5.9,3.0,5.1,1.9])
# apply model to all the sames
preds = apply_tree(model, features)
# generate confusion matrix, along with accuracy and kappa scores
confusion_matrix(labels, preds)
# get the probability of each label
apply_tree_proba(model, [5.9,3.0,5.1,1.9], ["Iris-setosa", "Iris-versicolor", "Iris-virginica"])
# run 3-fold cross validation of pruned tree,
n_folds=3
accuracy = nfoldCV_tree(labels, features, n_folds)
# set of classification parameters and respective default values
# pruning_purity: purity threshold used for post-pruning (default: 1.0, no pruning)
# max_depth: maximum depth of the decision tree (default: -1, no maximum)
# min_samples_leaf: the minimum number of samples each leaf needs to have (default: 1)
# min_samples_split: the minimum number of samples in needed for a split (default: 2)
# min_purity_increase: minimum purity needed for a split (default: 0.0)
# n_subfeatures: number of features to select at random (default: 0, keep all)
n_subfeatures=0; max_depth=-1; min_samples_leaf=1; min_samples_split=2
min_purity_increase=0.0; pruning_purity = 1.0
model = build_tree(labels, features,
n_subfeatures,
max_depth,
min_samples_leaf,
min_samples_split,
min_purity_increase)
accuracy = nfoldCV_tree(labels, features,
n_folds,
pruning_purity,
max_depth,
min_samples_leaf,
min_samples_split,
min_purity_increase)
```

Random Forest Classifier

```
# train random forest classifier
# using 2 random features, 10 trees, 0.5 portion of samples per tree, and a maximum tree depth of 6
model = build_forest(labels, features, 2, 10, 0.5, 6)
# apply learned model
apply_forest(model, [5.9,3.0,5.1,1.9])
# get the probability of each label
apply_forest_proba(model, [5.9,3.0,5.1,1.9], ["Iris-setosa", "Iris-versicolor", "Iris-virginica"])
# run 3-fold cross validation for forests, using 2 random features per split
n_folds=3; n_subfeatures=2
accuracy = nfoldCV_forest(labels, features, n_folds, n_subfeatures)
# set of classification parameters and respective default values
# n_subfeatures: number of features to consider at random per split (default: -1, sqrt(# features))
# n_trees: number of trees to train (default: 10)
# partial_sampling: fraction of samples to train each tree on (default: 0.7)
# max_depth: maximum depth of the decision trees (default: no maximum)
# min_samples_leaf: the minimum number of samples each leaf needs to have (default: 5)
# min_samples_split: the minimum number of samples in needed for a split (default: 2)
# min_purity_increase: minimum purity needed for a split (default: 0.0)
n_subfeatures=-1; n_trees=10; partial_sampling=0.7; max_depth=-1
min_samples_leaf=5; min_samples_split=2; min_purity_increase=0.0
model = build_forest(labels, features,
n_subfeatures,
n_trees,
partial_sampling,
max_depth,
min_samples_leaf,
min_samples_split,
min_purity_increase)
accuracy = nfoldCV_forest(labels, features,
n_folds,
n_subfeatures,
n_trees,
partial_sampling,
max_depth,
min_samples_leaf,
min_samples_split,
min_purity_increase)
```

Adaptive-Boosted Decision Stumps Classifier

```
# train adaptive-boosted stumps, using 7 iterations
model, coeffs = build_adaboost_stumps(labels, features, 7);
# apply learned model
apply_adaboost_stumps(model, coeffs, [5.9,3.0,5.1,1.9])
# get the probability of each label
apply_adaboost_stumps_proba(model, coeffs, [5.9,3.0,5.1,1.9], ["Iris-setosa", "Iris-versicolor", "Iris-virginica"])
# run 3-fold cross validation for boosted stumps, using 7 iterations
n_iterations=7; n_folds=3
accuracy = nfoldCV_stumps(labels, features,
n_folds,
n_iterations)
```

### Regression Example

```
n, m = 10^3, 5
features = randn(n, m)
weights = rand(-2:2, m)
labels = features * weights
```

Regression Tree

```
# train regression tree
model = build_tree(labels, features)
# apply learned model
apply_tree(model, [-0.9,3.0,5.1,1.9,0.0])
# run 3-fold cross validation, returns array of coefficients of determination (R^2)
n_folds = 3
r2 = nfoldCV_tree(labels, features, n_folds)
# set of regression parameters and respective default values
# pruning_purity: purity threshold used for post-pruning (default: 1.0, no pruning)
# max_depth: maximum depth of the decision tree (default: -1, no maximum)
# min_samples_leaf: the minimum number of samples each leaf needs to have (default: 5)
# min_samples_split: the minimum number of samples in needed for a split (default: 2)
# min_purity_increase: minimum purity needed for a split (default: 0.0)
# n_subfeatures: number of features to select at random (default: 0, keep all)
n_subfeatures = 0; max_depth = -1; min_samples_leaf = 5
min_samples_split = 2; min_purity_increase = 0.0; pruning_purity = 1.0
model = build_tree(labels, features,
n_subfeatures,
max_depth,
min_samples_leaf,
min_samples_split,
min_purity_increase)
r2 = nfoldCV_tree(labels, features,
n_folds,
pruning_purity,
max_depth,
min_samples_leaf,
min_samples_split,
min_purity_increase)
```

Regression Random Forest

```
# train regression forest, using 2 random features, 10 trees,
# averaging of 5 samples per leaf, and 0.7 portion of samples per tree
model = build_forest(labels, features, 2, 10, 0.7, 5)
# apply learned model
apply_forest(model, [-0.9,3.0,5.1,1.9,0.0])
# run 3-fold cross validation on regression forest, using 2 random features per split
n_subfeatures=2; n_folds=3
r2 = nfoldCV_forest(labels, features, n_folds, n_subfeatures)
# set of regression build_forest() parameters and respective default values
# n_subfeatures: number of features to consider at random per split (default: -1, sqrt(# features))
# n_trees: number of trees to train (default: 10)
# partial_sampling: fraction of samples to train each tree on (default: 0.7)
# max_depth: maximum depth of the decision trees (default: no maximum)
# min_samples_leaf: the minimum number of samples each leaf needs to have (default: 5)
# min_samples_split: the minimum number of samples in needed for a split (default: 2)
# min_purity_increase: minimum purity needed for a split (default: 0.0)
n_subfeatures=-1; n_trees=10; partial_sampling=0.7; max_depth=-1
min_samples_leaf=5; min_samples_split=2; min_purity_increase=0.0
model = build_forest(labels, features,
n_subfeatures,
n_trees,
partial_sampling,
max_depth,
min_samples_leaf,
min_samples_split,
min_purity_increase)
r2 = nfoldCV_forest(labels, features,
n_folds,
n_subfeatures,
n_trees,
partial_sampling,
max_depth,
min_samples_leaf,
min_samples_split,
min_purity_increase)
```

## Saving Models

Models can be saved to disk and loaded back with the use of the JLD2.jl package.

```
using JLD2
@save "model_file.jld2" model
```

Note that even though features and labels of type `Array{Any}`

are supported, it is highly recommended that data be cast to explicit types (ie with `float.(), string.()`

, etc). This significantly improves model training and prediction execution times, and also drastically reduces the size of saved models.