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Random Forest

Builds an ensemble of decision trees trained on random samples and feature subsets.

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Quick Facts

Compact metadata for implementation and discovery.

Category: Machine Learning
Difficulty: Intermediate
Family: Ensemble Learning
Tier: Core
Status: Verified
Review: Source Checked
Sources: 1
Formulas: 1
Relationships: 5
Code example: Not ready
Visualization: Ready

Overview

A random forest trains many decision trees on bootstrapped data and randomized feature choices. Predictions are aggregated by voting or averaging, reducing variance compared with a single tree.

Core Concepts

learned parametersmodel aggregationclass decision boundarytree structureensemble learningmodel fittraining examplesprediction rule

Quick facts

Complexity

Runtime and memory behavior at a glance.

Best

O(t n d log n)

Average

O(t n d log n)

Worst

O(t n^2 d)

Space

O(t n)

When to Use

Use when a strong nonparametric baseline is needed for tabular data.
Use when interpretability of individual splits is less important than ensemble accuracy.

When Not to Use

Avoid when model size or prediction latency must be very small.
Avoid when extrapolation beyond the training distribution is required.

What It Does

Samples training data for each tree
Randomizes feature choices during tree splits
Aggregates predictions across trees

Use Cases

Tabular classification and regression
Robust baselines for mixed feature sets
Estimating feature importance with caution

Inputs

Feature matrix
Target labels or values
Number of trees

Outputs

Ensemble model
Combined prediction

Key Formulas (1)

Forest vote

prediction = majority_vote(tree₁(x), tree₂(x), …, tree_n(x))

prediction = majority_vote(tree_1(x), tree_2(x), ..., tree_n(x))

Combines individual tree predictions into one ensemble prediction.

Pseudocode

1.For each tree in the ensemble
2.Sample training rows with replacement
3.Grow a decision tree using random feature subsets at splits
4.Store the trained tree
5.For prediction, aggregate tree votes or averages

Canonical Example

Input: training rows with features [age, income] and label approved/not approved
Output: many trees whose votes produce the final class
Explanation: Each tree sees a randomized view of the data, and the forest aggregates their predictions.

Implementation Notes

Keep preprocessing inside the train/validation split.
Tune tree count, depth, leaf size, and feature subsampling together.
Evaluate with out-of-bag or held-out metrics, not training accuracy.

Common Pitfalls

Leaking validation data through preprocessing gives inflated accuracy.
Too few trees can make results unstable.
Default feature-importance measures can be biased toward high-cardinality features.