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Artificial Intelligence (AI) Machine Learning

RandomForest

Lesson 9/19

Random Forest

Many decorrelated trees vote together. Bias stays similar, variance drops, and generalization improves.

Interactive simulation

Ensemble strength vs cost

Number of trees120.00

Max depth8.00

Feature subsampling ratio0.55

Bootstrap sample fraction0.72

Validation accuracy

98.0%

Variance reduction

82.0%

Inference cost

78.6%

Robustness

67.2%

Chart

Mathematical intuition

Bagging reduces variance

\hat{y}=\mathrm{mode}\{T_1(x), T_2(x), ..., T_B(x)\}

For classification, each tree votes and the majority wins.

\mathrm{Var}(\bar{T}) \approx \rho\sigma^2 + \frac{1-\rho}{B}\sigma^2

Lower inter-tree correlation $\rho$ + more trees $B$ means lower variance.

Step-by-step workflow

Input → Processing → Learning → Prediction → Output

Input

Training data

Processing

Bootstrap samples + feature subsets

Learning

Train many trees in parallel

Prediction

Aggregate votes / averages

Output

Final ensemble prediction

Code implementation

Python-style pseudocode

python

forest = []
for b in range(B):
    sample = bootstrap(train_data)
    tree = train_tree(sample, max_depth=max_depth, feature_subsample=feature_ratio)
    forest.append(tree)

def predict(x):
    votes = [tree.predict(x) for tree in forest]
    return majority(votes)

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