Decision Trees

Decision trees are one of the fundamental machine learning algorithms used for classification and regression tasks. They are extremely popular given their simplicity, interpretability, and versatility. In this post, we will provide a comprehensive overview of how decision trees work and their applications in machine learning systems.

We’ll cover:

• What are decision trees and how do they work?
• Decision tree algorithms - ID3, CART, C4.5
• Advantages and disadvantages
• Use cases and applications
• Ensemble methods like random forests and boosting
• Implementation in Python
• The future outlook

Let’s get started!

What are Decision Trees?

A decision tree is a supervised machine learning model for predicting target variables by learning simple decision rules inferred from data features.

Decision trees model data as a tree structure with nodes representing features/attributes, branches representing rules, and leaves representing outcomes. By traversing the tree from root to leaf nodes following the branches, we can classify new data points or predict their target values.

For example, a bank may use a decision tree to determine loan eligibility based on customer attributes like income, age, credit score, etc. These would be the nodes. Rules like “age > 25” and outcomes like “eligible”/”not eligible” form the branches and leaves respectively.

Based on a customer’s features, the tree is traversed from top to bottom to arrive at a loan eligibility prediction. Different customers will traverse different paths down the tree.

Decision trees mimic human decision-making more closely than other ML models. Their hierarchical structure makes it easy to interpret predictions. This interpretability is a key advantage of decision trees in applied ML.

How are Decision Trees Learned?

The key tasks when training a decision tree are:

1. Identifying the most predictive features to split on at each step.
2. Determining optimal thresholds for splitting continuous features.
3. Deciding when to stop splitting nodes into smaller branches.

This recursive process of identifying feature splits results in a learned tree structure that minimizes impurity from top to bottom. Impurity refers to how heterogeneous the labels are within a node in the tree. It decreases as we go from root to leaves.

Different decision tree algorithms use different metrics to select the optimal splits while building the tree. Let’s look at some popular algorithms next.

Decision Tree Algorithms

Many algorithms have been developed over the years for learning decision tree models from data. The most well-known include:

ID3

ID3 (Iterative Dichotomiser 3) was an early algorithm published in 1986. It creates decision trees top-down, greedy fashion by selecting the attribute with highest information gain at each step to split on.

Information gain measures how much adding a given attribute decreases the entropy (impurity) of the tree. Attributes that reduce impurity the most are chosen first.

ID3 cannot handle continuous features. It also does not support pruning the tree after creation. But it laid the foundation for other improved algorithms.

CART

Classification and Regression Trees (CART) was introduced in 1984 and improved upon ID3. Key features:

• Handles both categorical and continuous features.
• Uses Gini impurity to select split points.
• Performs backward pruning after creating large trees to avoid overfitting.
• Can learn regression trees for predicting continuous variables.

CART is widely used and implemented in packages like scikit-learn. It produces robust and interpretable trees efficiently.

C4.5

C4.5 is also an extension of ID3 developed in 1993. Key features:

• Uses information gain ratio to account for bias in multi-valued features.
• Handles missing values.
• Estimates error rates during pruning.
• Computes rulesets from trees for easy interpretation.

C4.5 is a popular benchmark algorithm for decision tree performance comparisons.

Many other variations and extensions exist, like CHAID, conditional inference trees, oblique trees, etc. This remains an active area of research in ML.

Advantages of Decision Trees

Decision tree models have characteristics that make them very useful for applied ML tasks:

Interpretability - The tree structure with rules provides a clear explanation for predictions.

Non-parametric - Make no assumptions about feature distributions. Handle nonlinearity well.

Computationally fast - Predictions have low inference latency by traversing trees. Fast to train.

Feature importance - Important splits occur higher up. Feature importances can be extracted.

Robust - Relatively resilient against outliers and noise. Ensemble methods improve robustness further.

Their intuitiveness and explainability has made decision trees very popular for initial prototyping and applied systems. They serve as the building blocks for powerful ensemble methods as well.

Disadvantages of Decision Trees

Decision trees do have some limitations to be aware of:

Overfitting - Greedy splitting can overfit trees to the training data. Regularization like pruning is required.

Data fragmentation - Continuous splitting creates leaf nodes with few samples. Increases variance.

Unstable - Small changes in data can result in very different tree structures. Ensembles reduces this variance.

Bias towards features with many splits - Information gain biases tree splitting towards features with more possible cut points.

When using decision trees, managing depth/splits carefully and pairing them with other techniques helps overcome these limitations.

Applications of Decision Trees

Here are some common applications that are a great fit for decision trees:

Classification - Discrete target variables. Fraud detection, spam detection, medical diagnosis, etc.

Regression - Continuous target variables. Price prediction, demand forecasting, algorithmic trading, etc.

Feature selection - Identifying most predictive features based on tree splits near the root node.

Recommendation systems - Traverse trees based on user attributes to recommend products.

Computer vision - Multi-stage classifiers for image classification and object detection.

Operational optimization - Asset utilization, production scheduling, dynamic pricing.

Decision trees lend themselves flexibly to a variety of predictive and descriptive tasks while keeping models interpretable.

Decision Tree Implementation in Python

Implementing decision trees from scratch is relatively straightforward. But we strongly recommend using existing libraries like scikit-learn for applying them in practice.

Here is an example workflow for classification with decision trees in Python:

# 1. Import decision tree classifier and datafrom sklearn.tree import DecisionTreeClassifierfrom sklearn.datasets import load_irisiris = load_iris()# 2. Fit classification treeclf = DecisionTreeClassifier()clf.fit(iris.data, iris.target)# 3. Predict new flower classclf.predict([[5.1, 3.8, 1.5, 0.4]])

Scikit-learn provides fine-grained control through parameters like max_depth, min_samples_leaf, and criterion to avoid overfitting.

Using the GraphViz export_graphviz function, trained trees can also be visualized for interpretation.

Decision Tree Ensembles

Ensemble methods combine multiple decision trees to improve overall predictive performance. They overcome overfitting and instability issues of single trees.

Popular ensembles include:

Random forests - Train multiple trees on random subsets of features, combining predictions by bagging or averaging.

Gradient boosting - Train decision trees sequentially to fix predecessor errors, merging them into powerful predictive models.

These ensemble techniques often achieve state-of-the-art results on ML benchmarks and competitions.

The Outlook for Decision Trees

Decision trees will continue thriving as a key predictive modeling tool given their uniqueness and advantages. Some promising research directions:

• Alternate split criteria and impurity measures to improve quality.
• Handling higher dimensionality data via forest sparsity regularization, conditional trees, etc.
• Online and adaptive tree learning for changing data streams and environments.
• Visualization and explainability of large decision tree ensembles.
• Incorporating neural networks for representation learning.

Tree-based models empower intuitive predictions explainable to human experts. This advantage will drive continued innovation in growing decision trees for years to come.

Key Takeaways

• Decision trees model data features as tree branches and outcomes as leaves.
• Algorithms like ID3, CART, C4.5 are used to learn optimal trees from training data.
• Trees are highly interpretable and handle nonlinearity, but prone to overfitting.
• Applications include classification, regression, recommendation, and more.
• Ensemble methods like random forests overcome limitations of single trees.
• Scikit-learn provides easy decision tree implementation in Python.
• The future is bright for growing innovation and applications of tree-based models.