Ensembles of Decision Trees

1. What are Ensembles?

Ensemble methods combine multiple machine learning models to create more powerful and robust models.
By aggregating the predictions of many models, ensembles typically achieve better generalization performance than any single model.
In the context of decision trees, ensembles combine multiple trees to overcome limitations of single trees such as overfitting and instability.

2. Why Ensemble Decision Trees?

Single decision trees:

Are easy to interpret but tend to overfit training data, leading to poor generalization,.
Can be unstable because small variations in data can change the structure of the tree significantly.

Ensemble methods exploit the idea that many weak learners (trees that individually overfit or only capture partial patterns) can be combined to form a strong learner by reducing variance and sometimes bias.

3. Two Main Types of Tree Ensembles

(a) Random Forests

Random forests are ensembles consisting of many decision trees.
Each tree is built on a bootstrap sample of the training data (sampling with replacement).
At each split in a tree, only a random subset of features is considered for splitting.
The aggregated prediction over all trees (majority vote for classification, average for regression) reduces overfitting by averaging diverse trees.

Key details:

Randomness ensures the trees differ; otherwise, correlated trees wouldn't reduce variance.
Trees grown are typically deeper than single decision trees because the random feature selection introduces diversity.
Random forests are powerful out-of-the-box models requiring minimal parameter tuning and usually do not require feature scaling.

(b) Gradient Boosted Decision Trees

Build trees sequentially, where each new tree tries to correct errors of the combined ensemble built so far.
Unlike random forests which average predictions, gradient boosting fits trees to the gradient of a loss function to gradually improve predictiveness.
This process often yields higher accuracy than random forests but training is more computationally intensive and sensitive to overfitting.

4. How Random Forests Inject Randomness

Data Sampling: Bootstrap sampling ensures each tree is trained on a different subset of data.
Feature Sampling: Each split considers only a subset of features randomly selected.

These two layers of randomness ensure:

Individual trees are less correlated.
Averaging predictions reduces variance and prevents overfitting seen in single deep trees.

5. Strengths of Ensembles of Trees

Robustness and accuracy: Reduced overfitting due to averaging or boosting.
Minimal assumptions: Like single trees, ensembles typically do not require feature scaling or extensive preprocessing.
Handle large feature spaces and data: Random forests can parallelize tree building and scale well.
Feature importance: Ensembles can provide measures of feature importance from aggregated trees.

6. Weaknesses and Considerations

Interpretability: Ensembles lose the straightforward interpretability of single trees. Hundreds of trees are hard to visualize and explain.
Computational cost: Training a large number of trees, especially with gradient boosting, can be time-consuming.
Parameter tuning: Gradient boosting requires careful tuning (learning rate, tree depth, number of trees) to avoid overfitting.

7. Summary Table for Random Forests and Gradient Boosting

Feature	Random Forests	Gradient Boosted Trees
Tree construction	Parallel, independent bootstrap samples	Sequential, residual fitting
Randomness	Data + feature sampling	Deterministic, based on gradients
Overfitting control	Averaging many decorrelated trees	Regularization, early stopping, shrinkage
Interpretability	Lower than single trees but feature importance available	Lower; complex, but feature importance measurable
Computation	Parallelizable; faster	Slower; sequential
Typical use cases	General-purpose, robust models	Performance-critical tasks, often winning in competitions

8. Additional Notes

Both methods build on the decision tree structure explained in detail,.
Random forests are often preferred as a baseline for structured data due to simplicity and effectiveness.
Gradient boosted trees can outperform random forests when carefully tuned but are less forgiving.

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