🌲 Random Forest

What is a Random Forest?

A Random Forest is a meta-algorithm that builds a collective of decision structures (trees) and aggregates their outcomes to form a more stable, generalized response. It leverages randomness both in data selection and feature consideration, aiming to reduce bias and variance simultaneously.

How does it operate?

• Stochastic construction: Multiple learners are instantiated using randomly sampled views of the original data.
• Independent reasoning: Each learner (tree) forms a distinct internal model based on local data and partial feature information.
• Synthesis of judgment: The ensemble's final output is derived by merging the diverse predictions—typically via averaging (regression) or voting (classification).

This creates a robust, noise-resistant estimator that thrives in high-dimensional, non-linear spaces.

How do Random Forests work?

A Random Forest works by building many simple decision trees and combining their results. Each tree is trained on a random subset of the data and uses a random selection of features. This randomness ensures that the trees are diverse. When it's time to make a prediction, each tree gives an answer, and the forest combines them—by majority vote for classification or averaging for regression. This collective decision-making helps reduce overfitting and makes the model more stable.
The parameter --n_estimators_randomforest controls how many decision trees are built in the forest. More trees can lead to better accuracy because the model has more opinions to average—but it also increases training time and memory usage.

What is a Decision Tree?

A Decision Tree is a simple, flowchart-like model that makes predictions by splitting the data into branches based on feature values. At each node, the tree chooses a feature and a threshold that best separates the data according to some criterion (like Gini impurity or information gain). This process continues until the data is fully split or a stopping condition is reached. In the end, each path through the tree leads to a leaf node that contains the predicted value or class. Decision Trees are easy to interpret but can easily overfit if used alone—this is why Random Forests combine many of them.

How does it guide parameter selection?

In optimization contexts:

• Model as proxy: The forest learns a representation of how parameter configurations map to performance metrics.
• Hypothesis generation: A space of candidate parameters is stochastically explored.
• Informed filtering: Candidates are scored by the model, ranking them by predicted utility.
• Constraint-aware selection: Top candidates are filtered through domain constraints before selection.

In essence, the Random Forest acts as a structured intuition engine—guiding the search for optimal configurations without direct evaluation of every possibility.

When and why to use it?

Random Forests excel in scenarios where:

• Data is noisy, sparse, or irregular.
• Black-box evaluation is expensive, and a quick approximation is preferred.
• Uncertainty estimates are not strictly required, or interpretability is more important than precision.
• Computation needs to remain light, or infrastructure is limited.

Compared to modular Bayesian approaches like BoTorch, Random Forests:

• Are faster to fit, especially with many categorical or discrete inputs.
• Can be more robust to small datasets and less sensitive to prior specification.

They are less suited when:

• Probabilistic modeling of the objective is central.
• Exploration–exploitation trade-offs need explicit control.
• Gradients or uncertainty quantification are essential to the problem structure.

In such cases, modular GP-based methods may be more appropriate—but at higher complexity and cost.