Random Forests

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🌲 Welcome to Random Forests

Random Forests are one of the most popular and powerful algorithms in machine learning. They solve Decision Trees' biggest problem (overfitting) by combining the predictions of multiple trees — hence the name "forest"!

The key insight: A group of imperfect predictions often beats a single perfect one. This phenomenon, called "wisdom of crowds," is the foundation of ensemble learning.

📊 Ensemble Learning: The Big Picture

Random Forests belong to the ensemble learning family, where multiple models combine to make better predictions than any single model.

🎯 What is a Random Forest?

🎲 The Wisdom of Crowds

Imagine asking 100 independent judges to vote on a criminal case. Even if each judge is only 60% accurate, the majority vote is likely to be correct!

🌲 Forest Analogy

Think of a forest ecosystem:

• 🌳 Individual Trees: Each tree is different (different data, different features)
• 🌲 Diversity: Different trees thrive under different conditions
• 🍃 Resilience: If one tree fails, the forest survives
• 🌍 Ecosystem Strength: The whole is greater than the sum of parts

Random Forests work because of three key mechanisms:

• Randomness: Each tree sees different data and features, reducing correlation
• Diversity: Different trees learn different patterns (low correlation between trees)
• Aggregation: Combining diverse predictions reduces errors (variance reduction)

⚙️ How Does Random Forest Work?

📋 The Algorithm (Step-by-Step)

🎲 Bootstrap Sampling Explained

\n Bootstrap sampling is sampling with replacement. This creates diverse training sets for each tree.\n

🎯 Feature Randomness

\n At each node split, Random Forests don't consider all features - only a random subset.\n

🗳️ Prediction Aggregation

📦 Out-of-Bag (OOB) Error

\n One of Random Forest's most clever features: built-in validation without a separate test set!\n

💻 Random Forest in Python

🎯 Complete Classification Example

# Complete Random Forest Classification: Iris Dataset
from sklearn.datasets import load_iris
from sklearn.ensemble import RandomForestClassifier
from sklearn.model_selection import train_test_split, cross_val_score
from sklearn.metrics import accuracy_score, classification_report, confusion_matrix
import matplotlib.pyplot as plt
import numpy as np

# Load dataset
iris = load_iris()
X, y = iris.data, iris.target

# Train/test split
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=42, stratify=y
)

print(f"Training samples: {len(X_train)}")
print(f"Test samples: {len(X_test)}")

# Create Random Forest
forest = RandomForestClassifier(
    n_estimators=100,        # Number of trees
    criterion='gini',        # or 'entropy'
    max_depth=None,          # Grow trees fully
    min_samples_split=2,
    min_samples_leaf=1,
    max_features='sqrt',     # √p features per split
    bootstrap=True,          # Use bootstrap samples
    oob_score=True,          # Calculate OOB error
    n_jobs=-1,               # Use all CPU cores
    random_state=42
)

# Train
forest.fit(X_train, y_train)

# Evaluate
train_acc = forest.score(X_train, y_train)
test_acc = forest.score(X_test, y_test)
oob_acc = forest.oob_score_

print(f"\\nTraining Accuracy: {train_acc:.2%}")
print(f"OOB Accuracy: {oob_acc:.2%}")  # Validation estimate
print(f"Test Accuracy: {test_acc:.2%}")

# Cross-validation
cv_scores = cross_val_score(forest, X_train, y_train, cv=5)
print(f"\\n5-Fold CV: {cv_scores.mean():.2%} (+/- {cv_scores.std() * 2:.2%})")

# Predictions
y_pred = forest.predict(X_test)
y_proba = forest.predict_proba(X_test)

print(f"\\nClassification Report:")
print(classification_report(y_test, y_pred, target_names=iris.target_names))

# Feature importance
print("\\n🌟 Feature Importance:")
importances = forest.feature_importances_
indices = np.argsort(importances)[::-1]
for i in indices:
    print(f"  {iris.feature_names[i]}: {importances[i]:.1%}")

📊 Regression Example: House Prices

# Random Forest Regression
from sklearn.ensemble import RandomForestRegressor
from sklearn.metrics import mean_squared_error, r2_score, mean_absolute_error
import numpy as np

# Sample data: [size_sqft, bedrooms, age_years, distance_to_city_km]
X_train = np.array([
    [1500, 3, 10, 5],
    [2000, 4, 5, 3],
    [1200, 2, 20, 8],
    [2500, 4, 2, 2],
    [1800, 3, 8, 6],
    [2200, 4, 3, 4],
    [1600, 3, 12, 7],
    [1900, 3, 6, 5]
])
y_train = np.array([250000, 350000, 180000, 420000, 300000, 380000, 240000, 320000])

# Train Random Forest Regressor
forest_reg = RandomForestRegressor(
    n_estimators=100,
    max_depth=10,
    min_samples_split=2,
    oob_score=True,
    random_state=42
)
forest_reg.fit(X_train, y_train)

# Predictions
new_houses = np.array([
    [1700, 3, 12, 6],
    [2300, 4, 1, 2]
])
predictions = forest_reg.predict(new_houses)

print("House Price Predictions:")
for i, pred in enumerate(predictions, 1):
    print(f"  House {i}: ${pred:,.0f}")

# Model performance
train_pred = forest_reg.predict(X_train)
mse = mean_squared_error(y_train, train_pred)
rmse = np.sqrt(mse)
mae = mean_absolute_error(y_train, train_pred)
r2 = r2_score(y_train, train_pred)

print(f"\\nModel Performance:")
print(f"  RMSE: ${rmse:,.0f}")
print(f"  MAE: ${mae:,.0f}")
print(f"  R² Score: {r2:.2%}")
print(f"  OOB Score: {forest_reg.oob_score_:.2%}")

# Feature importance
features = ['Size (sqft)', 'Bedrooms', 'Age (years)', 'Distance (km)']
print("\\n🏠 Feature Importance:")
for feat, imp in zip(features, forest_reg.feature_importances_):
    print(f"  {feat}: {imp:.1%}")

📈 Visualizing Random Forests

# Visualization 1: Feature Importance Bar Chart
import matplotlib.pyplot as plt

importances = forest.feature_importances_
indices = np.argsort(importances)[::-1]

plt.figure(figsize=(10, 6))
plt.title("Feature Importance in Random Forest")
plt.bar(range(X.shape[1]), importances[indices])
plt.xticks(range(X.shape[1]), [iris.feature_names[i] for i in indices], rotation=45)
plt.ylabel('Importance')
plt.xlabel('Feature')
plt.tight_layout()
plt.show()

# Visualization 2: Number of Trees vs Performance
train_scores = []
oob_scores = []
tree_counts = range(1, 201, 10)

for n_trees in tree_counts:
    rf = RandomForestClassifier(n_estimators=n_trees, oob_score=True, random_state=42)
    rf.fit(X_train, y_train)
    train_scores.append(rf.score(X_train, y_train))
    oob_scores.append(rf.oob_score_)

plt.figure(figsize=(10, 6))
plt.plot(tree_counts, train_scores, label='Training Accuracy', marker='o')
plt.plot(tree_counts, oob_scores, label='OOB Accuracy', marker='s')
plt.xlabel('Number of Trees')
plt.ylabel('Accuracy')
plt.title('Random Forest: Performance vs Number of Trees')
plt.legend()
plt.grid(True, alpha=0.3)
plt.show()

# Visualization 3: Decision Boundaries (2D)
from matplotlib.colors import ListedColormap

# Use only 2 features for 2D visualization
X_2d = X[:, [2, 3]]  # petal length, petal width
y_binary = (y == 2).astype(int)  # Virginica vs others

X_train_2d, X_test_2d, y_train_bin, y_test_bin = train_test_split(
    X_2d, y_binary, test_size=0.2, random_state=42
)

forest_2d = RandomForestClassifier(n_estimators=100, random_state=42)
forest_2d.fit(X_train_2d, y_train_bin)

# Create mesh
x_min, x_max = X_2d[:, 0].min() - 0.5, X_2d[:, 0].max() + 0.5
y_min, y_max = X_2d[:, 1].min() - 0.5, X_2d[:, 1].max() + 0.5
xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.02),
                     np.arange(y_min, y_max, 0.02))

Z = forest_2d.predict(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)

plt.figure(figsize=(10, 6))
plt.contourf(xx, yy, Z, alpha=0.4, cmap=ListedColormap(['#FFAAAA', '#AAAAFF']))
plt.scatter(X_2d[:, 0], X_2d[:, 1], c=y_binary, cmap=ListedColormap(['#FF0000', '#0000FF']),
            edgecolor='black', s=50)
plt.xlabel('Petal Length (cm)')
plt.ylabel('Petal Width (cm)')
plt.title('Random Forest Decision Boundaries')
plt.colorbar()
plt.show()

# Visualization 4: Individual Tree Inspection
from sklearn.tree import plot_tree

# Visualize one tree from the forest
plt.figure(figsize=(20, 10))
plot_tree(
    forest.estimators_[0],  # First tree
    feature_names=iris.feature_names,
    class_names=iris.target_names,
    filled=True,
    max_depth=3  # Only show first 3 levels
)
plt.title("Single Tree from Random Forest (Depth 3)")
plt.tight_layout()
plt.show()

🔧 Comparing Random Forest vs Decision Tree

# Head-to-Head Comparison
from sklearn.tree import DecisionTreeClassifier

# Decision Tree (single)
tree = DecisionTreeClassifier(max_depth=5, random_state=42)
tree.fit(X_train, y_train)

# Random Forest
forest = RandomForestClassifier(n_estimators=100, max_depth=5, random_state=42, oob_score=True)
forest.fit(X_train, y_train)

# Comparison
print("Performance Comparison:")
print(f"\\nDecision Tree:")
print(f"  Training: {tree.score(X_train, y_train):.2%}")
print(f"  Test: {tree.score(X_test, y_test):.2%}")
print(f"  Difference: {tree.score(X_train, y_train) - tree.score(X_test, y_test):.2%} (overfitting)")

print(f"\\nRandom Forest:")
print(f"  Training: {forest.score(X_train, y_train):.2%}")
print(f"  OOB: {forest.oob_score_:.2%}")
print(f"  Test: {forest.score(X_test, y_test):.2%}")
print(f"  Difference: {forest.score(X_train, y_train) - forest.score(X_test, y_test):.2%} (less overfitting)")

# Stability test: Train multiple times with different random states
tree_scores = []
forest_scores = []

for seed in range(10):
    X_tr, X_te, y_tr, y_te = train_test_split(X, y, test_size=0.2, random_state=seed)
    
    tree = DecisionTreeClassifier(max_depth=5, random_state=42)
    tree.fit(X_tr, y_tr)
    tree_scores.append(tree.score(X_te, y_te))
    
    forest = RandomForestClassifier(n_estimators=100, max_depth=5, random_state=42)
    forest.fit(X_tr, y_tr)
    forest_scores.append(forest.score(X_te, y_te))

print(f"\\nStability Across 10 Different Train/Test Splits:")
print(f"Decision Tree: {np.mean(tree_scores):.2%} (+/- {np.std(tree_scores):.2%})")
print(f"Random Forest: {np.mean(forest_scores):.2%} (+/- {np.std(forest_scores):.2%})")
print(f"\\nRandom Forest is {np.std(tree_scores)/np.std(forest_scores):.1f}x more stable!")

🎨 Hyperparameter Tuning Guide

📊 Key Hyperparameters Explained

🎯 Hyperparameter Tuning Strategy

# Method 1: Manual Tuning (Start Here)
from sklearn.ensemble import RandomForestClassifier

# Good starting point for most problems
forest = RandomForestClassifier(
    n_estimators=100,        # Usually enough
    max_depth=None,          # Let trees grow fully
    max_features='sqrt',     # Default for classification
    min_samples_split=2,     # Default
    min_samples_leaf=1,      # Default
    bootstrap=True,
    oob_score=True,          # Get free validation score
    n_jobs=-1,               # Use all CPU cores
    random_state=42
)
forest.fit(X_train, y_train)

print(f"OOB Score: {forest.oob_score_:.2%}")
print(f"Test Score: {forest.score(X_test, y_test):.2%}")

# Method 2: GridSearchCV (Exhaustive Search)
from sklearn.model_selection import GridSearchCV

param_grid = {
    'n_estimators': [100, 200, 500],
    'max_depth': [10, 20, None],
    'max_features': ['sqrt', 'log2'],
    'min_samples_split': [2, 5, 10],
    'min_samples_leaf': [1, 2, 4]
}

grid_search = GridSearchCV(
    RandomForestClassifier(random_state=42),
    param_grid,
    cv=5,
    scoring='accuracy',
    n_jobs=-1,
    verbose=1
)
grid_search.fit(X_train, y_train)

print(f"\\nBest parameters: {grid_search.best_params_}")
print(f"Best CV score: {grid_search.best_score_:.2%}")
print(f"Test score: {grid_search.score(X_test, y_test):.2%}")

# Method 3: RandomizedSearchCV (Faster Alternative)
from sklearn.model_selection import RandomizedSearchCV
from scipy.stats import randint

param_dist = {
    'n_estimators': randint(100, 1000),
    'max_depth': [10, 20, 30, None],
    'max_features': ['sqrt', 'log2', None],
    'min_samples_split': randint(2, 20),
    'min_samples_leaf': randint(1, 10)
}

random_search = RandomizedSearchCV(
    RandomForestClassifier(random_state=42),
    param_distributions=param_dist,
    n_iter=50,  # Try 50 random combinations
    cv=5,
    scoring='accuracy',
    n_jobs=-1,
    random_state=42
)
random_search.fit(X_train, y_train)

print(f"\\nBest parameters: {random_search.best_params_}")
print(f"Best CV score: {random_search.best_score_:.2%}")

💡 Tuning Guidelines

✅ Strengths & ❌ Limitations

🔧 Troubleshooting Guide

🐛 Common Code Issues

# ❌ WRONG: Not using all CPU cores
forest = RandomForestClassifier(n_estimators=1000)  # Will take forever!

# ✅ RIGHT: Parallelize training
forest = RandomForestClassifier(n_estimators=1000, n_jobs=-1)

# ❌ WRONG: Ignoring OOB score
forest = RandomForestClassifier(n_estimators=100)
forest.fit(X_train, y_train)
# Missing free validation!

# ✅ RIGHT: Use OOB for validation
forest = RandomForestClassifier(n_estimators=100, oob_score=True)
forest.fit(X_train, y_train)
print(f"OOB Score: {forest.oob_score_:.2%}")

# ❌ WRONG: Extensive hyperparameter tuning
# Spending hours tuning when defaults work fine

# ✅ RIGHT: Start with defaults, tune only if needed
forest = RandomForestClassifier()  # Defaults are excellent!

# ❌ WRONG: Setting bootstrap=False
forest = RandomForestClassifier(bootstrap=False)
# This breaks the bagging mechanism!

# ✅ RIGHT: Always use bootstrap (default)
forest = RandomForestClassifier(bootstrap=True)

🚀 Practice Projects

📝 Project Starter Template

# Random Forest Project Template
from sklearn.ensemble import RandomForestClassifier
from sklearn.model_selection import train_test_split, cross_val_score
from sklearn.metrics import accuracy_score, classification_report, confusion_matrix
import pandas as pd
import numpy as np

# 1. Load and explore data
# df = pd.read_csv('your_dataset.csv')
# X = df.drop('target', axis=1)
# y = df['target']

# 2. Data preprocessing
# - Handle missing values
# - Encode categorical features
# - Feature engineering

# 3. Train/test split
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=42, stratify=y
)

# 4. Train Random Forest (start with defaults!)
forest = RandomForestClassifier(
    n_estimators=100,
    oob_score=True,
    n_jobs=-1,
    random_state=42
)
forest.fit(X_train, y_train)

# 5. Evaluate
print(f"Training Accuracy: {forest.score(X_train, y_train):.2%}")
print(f"OOB Accuracy: {forest.oob_score_:.2%}")
print(f"Test Accuracy: {forest.score(X_test, y_test):.2%}")

# 6. Cross-validation
cv_scores = cross_val_score(forest, X_train, y_train, cv=5)
print(f"\\nCV Accuracy: {cv_scores.mean():.2%} (+/- {cv_scores.std()*2:.2%})")

# 7. Feature importance
importances = pd.DataFrame({
    'feature': X.columns,
    'importance': forest.feature_importances_
}).sort_values('importance', ascending=False)
print(f"\\n🌟 Top 10 Features:")
print(importances.head(10))

# 8. Detailed metrics
y_pred = forest.predict(X_test)
print(f"\\nClassification Report:")
print(classification_report(y_test, y_pred))

# 9. (Optional) Hyperparameter tuning
# from sklearn.model_selection import GridSearchCV
# param_grid = {'n_estimators': [100, 200, 500]}
# grid = GridSearchCV(forest, param_grid, cv=5)
# grid.fit(X_train, y_train)

📋 Summary

✅ What You've Learned:

🎓 Key Takeaways

🔑 Quick Reference Card

# Random Forest Essentials Cheat Sheet

# Classification
from sklearn.ensemble import RandomForestClassifier
forest = RandomForestClassifier(
    n_estimators=100,      # Number of trees
    max_depth=None,        # Unlimited depth
    max_features='sqrt',   # √p features per split
    min_samples_split=2,   # Default
    min_samples_leaf=1,    # Default
    bootstrap=True,        # Use bagging
    oob_score=True,        # Get OOB error
    n_jobs=-1,             # Parallel processing
    random_state=42
)
forest.fit(X_train, y_train)

# Regression
from sklearn.ensemble import RandomForestRegressor
forest_reg = RandomForestRegressor(
    n_estimators=100,
    max_features='auto'    # p/3 for regression
)

# Key Methods
forest.predict(X_test)              # Predictions
forest.predict_proba(X_test)        # Probabilities
forest.feature_importances_         # Importance
forest.oob_score_                   # OOB validation
forest.estimators_                  # Access individual trees

# Quick Evaluation
print(f"OOB: {forest.oob_score_:.2%}")
print(f"Test: {forest.score(X_test, y_test):.2%}")

# Hyperparameter Tuning (if needed)
from sklearn.model_selection import RandomizedSearchCV
params = {
    'n_estimators': [100, 200, 500],
    'max_depth': [10, 20, None]
}
search = RandomizedSearchCV(forest, params, n_iter=10, cv=5)
search.fit(X_train, y_train)

🚀 What's Next?

In the next tutorial, Support Vector Machines, we'll learn a completely different approach: finding optimal boundaries that maximize the margin between classes. Different philosophy, often superior results on smaller datasets!