Tree-Based Models Using R

Tree-based models are a popular class of algorithms for machine learning tasks. These models use decision trees to model relationships between variables and make predictions. In R Programming Language, there are several packages that can be used to create and work with tree-based models, including ‘rpart’, ‘party’, and ‘randomForest’. In this article, we will explore these packages and demonstrate how to use them for various tasks.

What are Tree-Based Models?

Tree-based models are a type of supervised learning algorithm that can be used for both classification and regression tasks. These models work by breaking down a dataset into smaller and smaller subsets while at the same time creating a tree-like structure of decisions that ultimately leads to a prediction. At each node of the tree, a decision is made based on the value of a single input variable. Depending on the value of this variable, the algorithm follows one of two paths, and the process continues until a final prediction is made.

The main advantage of tree-based models is their interpretability. Because the model is represented as a tree of decisions, it is easy to understand and visualize how the algorithm arrived at its prediction. This makes it useful for domains where understanding the reasons behind a decision is essential, such as medicine or finance.

Decision Tree

A Decision Tree is a popular supervised machine learning algorithm that is used for both classification and regression tasks. It is a tree-like model where each internal node represents a feature or attribute, each branch represents a decision rule or condition, and each leaf node represents a prediction or a class label. The Decision Tree algorithm recursively partitions the data based on the values of features and selects the best-split criteria to minimize the impurity or maximize the information gain. Decision Trees are simple to understand, interpret, and visualize, and can handle both categorical and numerical data.

R

library(rpart)
data(iris)

# create decision tree
iris.tree <- rpart(Species ~ ., data = iris,
                   method = "class")

# plot decision tree
plot(iris.tree, main = "Decision Tree for Iris Dataset")
text(iris.tree, use.n = TRUE,
     all = TRUE, cex = 0.8)

Output:

Decision tree for iris dataset

R

library(party)
library(MASS)
data(Boston)

# create decision tree
boston.tree <- ctree(medv ~ ., data = Boston)

# plot decision tree
plot(boston.tree,
     main = "Decision Tree for Boston Housing Dataset")

Output:

Decision tree for Boston housing dataset

Regression Trees vs Classification Trees

Decision Trees can be further classified into Regression Trees and Classification Trees based on their output type. A Regression Tree is used when the output variable is continuous or numerical, and the goal is to predict a numerical value. The leaf nodes of a Regression Tree represent the predicted values, and the objective is to minimize the sum of squared errors between the predicted values and actual values. On the other hand, a Classification Tree is used when the output variable is categorical or discrete, and the goal is to predict the class label of an observation. The leaf nodes of a Classification Tree represent the predicted class labels, and the objective is to minimize the misclassification rate or maximize the purity of the node.

Random Forest

Random Forest is an ensemble learning method that combines multiple Decision Trees to improve performance and reduce overfitting. It randomly samples the data and features and trains multiple Decision Trees on different subsets of the data. During prediction, the Random Forest aggregates the predictions of all the Decision Trees to make a final prediction. Random Forest is a powerful algorithm that can handle high-dimensional and noisy data and can handle both classification and regression tasks. It is widely used in various applications such as image recognition, text classification, and bioinformatics.

Tree-based algorithms, such as Decision Trees, Regression Trees, and Random Forest, are based on a hierarchical structure consisting of nodes and branches. Here are some of the commonly used terminologies associated with tree-based algorithms:

1. Root Node: The topmost node in a tree is called the root node, and it represents the entire dataset or population.
2. Leaf Node: The leaf nodes are the terminal nodes of the tree, representing the final outcome or prediction. A leaf node does not have any child nodes.
3. Branch: The branches represent the decisions or rules based on the values of features. The branches connect the nodes to other nodes or leaf nodes.
4. Sub-Tree: A sub-tree is a tree structure that is a part of the larger tree. It is created by partitioning the data based on a specific feature.
5. Child Node: The nodes that are connected to a parent node through a branch are called child nodes. Each parent node can have multiple child nodes.
6. Split: A split is the decision point or the condition used to partition the data at a node. It is based on the values of the features.
7. Depth: The depth of a tree is the number of layers between the root node and the deepest leaf node. It represents the complexity of the tree.
8. Pruning: Pruning is a process of removing unnecessary nodes and branches from a tree to prevent overfitting and improve the generalization ability of the model.
9. Impurity: Impurity is a measure of the homogeneity or purity of the data at a node. In classification trees, impurity is measured using metrics such as Gini Index, Entropy, and Classification Error. In regression trees, impurity is measured using metrics such as Mean Squared Error (MSE) or Mean Absolute Error (MAE). The goal is to minimize the impurity or maximize the purity of the node.
10. Feature Importance: Feature Importance is a measure of the contribution of each feature in the model. It represents how much each feature reduces the impurity or improves the performance of the model.

R

library(randomForest)
data(iris)

# create random forest
iris.rf <- randomForest(Species ~ .,
                        data = iris)

# plot variable importance
varImpPlot(iris.rf)

Output:

Variable importance plot for the iris dataset

Ensemble methods

Ensemble methods are machine learning techniques that combine multiple models to improve the overall performance and reduce the variance of the model. Tree-based algorithms can benefit from ensemble methods, such as Bagging and Boosting algorithms.

Bagging (Bootstrap Aggregating) Algorithm

Bagging is an ensemble method that creates multiple models by resampling the data with replacement and then aggregating the results of each model. In the context of tree-based algorithms, bagging can be applied to a Random Forest, where each model is a Decision Tree trained on a bootstrap sample of the data. The output of the Random Forest is the average of the predictions of all the trees, which reduces the overfitting and improves the performance of the model.

Boosting Algorithm

Boosting is an ensemble method that creates multiple models by iteratively improving the performance of the previous models. The boosting algorithm assigns weights to each data point based on its importance and trains a weak learner on the weighted data. Then, it updates the weights based on the misclassified data and trains another weak learner on the updated weights. This process is repeated until a predetermined number of models is reached or until the performance of the model stops improving. In the context of tree-based algorithms, boosting can be applied to Gradient Boosting Machines (GBM) and Extreme Gradient Boosting (XGBoost) algorithms.

Gradient Boosting Machine (GBM)

GBM is a boosting algorithm that creates an ensemble of Decision Trees by iteratively minimizing the loss function. The GBM algorithm first trains a Decision Tree on the data and then calculates the residuals or errors of the model. Then, it trains another Decision Tree on the residuals and adds the predictions of the new model to the previous model. This process is repeated until a predetermined number of models is reached or until the performance of the model stops improving. GBM is a powerful algorithm that can handle both regression and classification tasks and can be customized by changing the hyperparameters.

Extreme Gradient Boosting (XGBoost)

XGBoost is an optimized version of the GBM algorithm that uses a gradient-boosting approach to improve performance and reduce training time. XGBoost employs several techniques, such as parallel processing, regularization, and tree pruning, to improve the speed and accuracy of the algorithm. XGBoost can handle large datasets, high-dimensional data, and missing values, and can be used for both regression and classification tasks. It is widely used in various applications, such as image recognition, natural language processing, and time-series forecasting.