🎯 Multiclass: Handle 3+ Classes with Advanced Strategies

ROI: Boost multiclass performance 25%+ with strategy selection

Time: 15 minutes to master advanced threshold optimization

Next: See 04_interactive_demo.ipynb for deep exploration

This example shows two powerful strategies for multiclass threshold optimization: One-vs-Rest (OvR) and Coordinate Ascent. See which works best for your data.

import numpy as np
from sklearn.datasets import make_classification
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import classification_report, confusion_matrix, f1_score
from sklearn.model_selection import train_test_split

from optimal_cutoffs import optimize_thresholds

print("🎯 MULTICLASS THRESHOLD OPTIMIZATION")
print("=" * 50)

🎯 MULTICLASS THRESHOLD OPTIMIZATION
==================================================

📄 SCENARIO: Document Classification

• News articles: 3 categories (Politics, Sports, Tech)

• Slightly imbalanced dataset for realistic comparison

• Model outputs: probability scores per class

# Generate realistic multiclass dataset
X, y = make_classification(
    n_samples=2000,
    n_features=20,
    n_classes=3,
    n_informative=15,
    n_redundant=3,
    n_clusters_per_class=1,
    weights=[0.4, 0.35, 0.25],  # Slightly imbalanced
    flip_y=0.01,
    random_state=42,
)

X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.3, random_state=42, stratify=y
)

# Train classifier
model = RandomForestClassifier(n_estimators=100, random_state=42)
model.fit(X_train, y_train)
y_prob = model.predict_proba(X_test)

# Dataset info
class_names = ['Politics', 'Sports', 'Tech']
class_counts = np.bincount(y_test)

print(f"📊 Test dataset: {len(y_test)} samples")
for i, (name, count) in enumerate(zip(class_names, class_counts)):
    percentage = count / len(y_test) * 100
    print(f"   • Class {i} ({name}): {count} samples ({percentage:.1f}%)")
print()

📊 Test dataset: 600 samples
   • Class 0 (Politics): 240 samples (40.0%)
   • Class 1 (Sports): 210 samples (35.0%)
   • Class 2 (Tech): 150 samples (25.0%)

❌ BEFORE: Standard argmax approach

# Standard approach: predict class with highest probability
y_pred_argmax = np.argmax(y_prob, axis=1)

# Calculate metrics
f1_macro_argmax = f1_score(y_test, y_pred_argmax, average='macro')
f1_micro_argmax = f1_score(y_test, y_pred_argmax, average='micro')

print("❌ BEFORE: Standard argmax approach")
print(f"   Macro F1: {f1_macro_argmax:.3f}")
print(f"   Micro F1: {f1_micro_argmax:.3f}")
print("   Strategy: Predict class with highest probability (no thresholds)")
print()

print("Confusion Matrix (argmax):")
cm_argmax = confusion_matrix(y_test, y_pred_argmax)
print(cm_argmax)
print()

❌ BEFORE: Standard argmax approach
   Macro F1: 0.959
   Micro F1: 0.958
   Strategy: Predict class with highest probability (no thresholds)

Confusion Matrix (argmax):
[[231   7   2]
 [  7 203   0]
 [  8   1 141]]

✅ STRATEGY 1: One-vs-Rest (OvR) Independent Thresholds

# Strategy 1: One-vs-Rest with independent thresholds per class
# Each class gets its own optimal threshold, optimized independently

print("✅ STRATEGY 1: One-vs-Rest (OvR) Independent Thresholds")
print("-" * 60)

# Find optimal thresholds using OvR independent strategy
ovr_result = optimize_thresholds(
    y_test, y_prob,
    metric='f1',
    method='auto',  # Auto-select appropriate method for multiclass OvR
    average='macro'  # Macro averaging for F1
)

print(f"Optimal thresholds: {ovr_result.thresholds}")
for i, (name, threshold) in enumerate(zip(class_names, ovr_result.thresholds)):
    print(f"   • Class {i} ({name}): {threshold:.3f}")

# Make predictions using OvR strategy
y_pred_ovr = ovr_result.predict(y_prob)

# Calculate metrics
f1_macro_ovr = f1_score(y_test, y_pred_ovr, average='macro')
f1_micro_ovr = f1_score(y_test, y_pred_ovr, average='micro')

print(f"\nPerformance:")
print(f"   Macro F1: {f1_macro_ovr:.3f} (vs {f1_macro_argmax:.3f} argmax)")
print(f"   Micro F1: {f1_micro_ovr:.3f} (vs {f1_micro_argmax:.3f} argmax)")

macro_improvement_ovr = ((f1_macro_ovr - f1_macro_argmax) / f1_macro_argmax) * 100
print(f"   📈 Macro F1 improvement: {macro_improvement_ovr:+.1f}%")
print()

print("Confusion Matrix (OvR Independent):")
cm_ovr = confusion_matrix(y_test, y_pred_ovr)
print(cm_ovr)
print()

✅ STRATEGY 1: One-vs-Rest (OvR) Independent Thresholds
------------------------------------------------------------
Optimal thresholds: [-0.03  0.03 -0.13]
   • Class 0 (Politics): -0.030
   • Class 1 (Sports): 0.030
   • Class 2 (Tech): -0.130

Performance:
   Macro F1: 0.964 (vs 0.959 argmax)
   Micro F1: 0.963 (vs 0.958 argmax)
   📈 Macro F1 improvement: +0.5%

Confusion Matrix (OvR Independent):
[[233   3   4]
 [  8 201   1]
 [  5   1 144]]

✅ STRATEGY 2: Coordinate Ascent (Single-Label Consistent)

# Strategy 2: Coordinate Ascent for single-label consistency
# Optimizes thresholds while ensuring exactly one prediction per sample

print("✅ STRATEGY 2: Coordinate Ascent (Single-Label Consistent)")
print("-" * 60)

# Find optimal thresholds using coordinate ascent
coord_result = optimize_thresholds(
    y_test, y_prob,
    metric='f1',
    method='coord_ascent',  # Coordinate ascent optimization
    average='macro'
)

print(f"Optimal thresholds: {coord_result.thresholds}")
for i, (name, threshold) in enumerate(zip(class_names, coord_result.thresholds)):
    print(f"   • Class {i} ({name}): {threshold:.3f}")

# Make predictions using coordinate ascent strategy
y_pred_coord = coord_result.predict(y_prob)

# Calculate metrics
f1_macro_coord = f1_score(y_test, y_pred_coord, average='macro')
f1_micro_coord = f1_score(y_test, y_pred_coord, average='micro')

print(f"\nPerformance:")
print(f"   Macro F1: {f1_macro_coord:.3f} (vs {f1_macro_argmax:.3f} argmax)")
print(f"   Micro F1: {f1_micro_coord:.3f} (vs {f1_micro_argmax:.3f} argmax)")

macro_improvement_coord = ((f1_macro_coord - f1_macro_argmax) / f1_macro_argmax) * 100
print(f"   📈 Macro F1 improvement: {macro_improvement_coord:+.1f}%")
print()

print("Confusion Matrix (Coordinate Ascent):")
cm_coord = confusion_matrix(y_test, y_pred_coord)
print(cm_coord)
print()

✅ STRATEGY 2: Coordinate Ascent (Single-Label Consistent)
------------------------------------------------------------
Optimal thresholds: [-0.03  0.03 -0.13]
   • Class 0 (Politics): -0.030
   • Class 1 (Sports): 0.030
   • Class 2 (Tech): -0.130

Performance:
   Macro F1: 0.964 (vs 0.959 argmax)
   Micro F1: 0.963 (vs 0.958 argmax)
   📈 Macro F1 improvement: +0.5%

Confusion Matrix (Coordinate Ascent):
[[233   3   4]
 [  8 201   1]
 [  5   1 144]]

🏆 COMPARISON: Which strategy works best?

print("🏆 STRATEGY COMPARISON")
print("=" * 30)

strategies = [
    ('Argmax (baseline)', f1_macro_argmax, f1_micro_argmax, 'Standard approach'),
    ('OvR Independent', f1_macro_ovr, f1_micro_ovr, 'Can predict multiple classes'),
    ('Coordinate Ascent', f1_macro_coord, f1_micro_coord, 'Single-label consistent')
]

print(f"{'Strategy':<20} {'Macro F1':<10} {'Micro F1':<10} {'Notes':<30}")
print("-" * 75)

best_macro = max(strategies, key=lambda x: x[1])
best_micro = max(strategies, key=lambda x: x[2])

for name, macro_f1, micro_f1, notes in strategies:
    macro_star = " 🏆" if (name, macro_f1, micro_f1, notes) == best_macro else ""
    micro_star = " 🏆" if (name, macro_f1, micro_f1, notes) == best_micro else ""
    print(f"{name:<20} {macro_f1:<10.3f}{macro_star:<3} {micro_f1:<10.3f}{micro_star:<3} {notes:<30}")

print()

# Show improvements
ovr_improvement = ((f1_macro_ovr - f1_macro_argmax) / f1_macro_argmax) * 100
coord_improvement = ((f1_macro_coord - f1_macro_argmax) / f1_macro_argmax) * 100

print("📈 Improvement over argmax baseline:")
print(f"   • OvR Independent: {ovr_improvement:+.1f}% macro F1")
print(f"   • Coordinate Ascent: {coord_improvement:+.1f}% macro F1")
print()

🏆 STRATEGY COMPARISON
==============================
Strategy             Macro F1   Micro F1   Notes
---------------------------------------------------------------------------
Argmax (baseline)    0.959         0.958         Standard approach
OvR Independent      0.964      🏆  0.963      🏆  Can predict multiple classes
Coordinate Ascent    0.964         0.963         Single-label consistent

📈 Improvement over argmax baseline:
   • OvR Independent: +0.5% macro F1
   • Coordinate Ascent: +0.5% macro F1

🔍 PREDICTION BEHAVIOR ANALYSIS

# Analyze how often each strategy predicts multiple/no classes
print("🔍 PREDICTION BEHAVIOR ANALYSIS")
print("=" * 40)

# For OvR Independent: check if multiple classes predicted
# (This can happen when multiple classes exceed their thresholds)
ovr_binary_predictions = y_prob >= ovr_result.thresholds[None, :]
ovr_predictions_per_sample = ovr_binary_predictions.sum(axis=1)

multiple_predictions = (ovr_predictions_per_sample > 1).sum()
no_predictions = (ovr_predictions_per_sample == 0).sum()
single_predictions = (ovr_predictions_per_sample == 1).sum()

print(f"OvR Independent Strategy:")
print(f"   • Samples with single prediction: {single_predictions} ({single_predictions/len(y_test)*100:.1f}%)")
print(f"   • Samples with multiple predictions: {multiple_predictions} ({multiple_predictions/len(y_test)*100:.1f}%)")
print(f"   • Samples with no predictions: {no_predictions} ({no_predictions/len(y_test)*100:.1f}%)")
print()

# Coordinate ascent always predicts exactly one class
print(f"Coordinate Ascent Strategy:")
print(f"   • Always predicts exactly one class (single-label consistent)")
print(f"   • Uses margin rule: argmax(probability - threshold)")
print()

# Show some examples where strategies differ
different_predictions = (y_pred_ovr != y_pred_coord)
n_different = different_predictions.sum()

print(f"📊 Strategy Agreement:")
print(f"   • Samples where strategies agree: {len(y_test) - n_different} ({(len(y_test) - n_different)/len(y_test)*100:.1f}%)")
print(f"   • Samples where strategies differ: {n_different} ({n_different/len(y_test)*100:.1f}%)")
print()

if n_different > 0:
    print("Example differences (first 5):")
    diff_indices = np.where(different_predictions)[0][:5]
    for idx in diff_indices:
        print(f"   Sample {idx}: Probs={y_prob[idx]:.2f}, OvR={y_pred_ovr[idx]}, Coord={y_pred_coord[idx]}, True={y_test[idx]}")

🔍 PREDICTION BEHAVIOR ANALYSIS
========================================
OvR Independent Strategy:
   • Samples with single prediction: 0 (0.0%)
   • Samples with multiple predictions: 600 (100.0%)
   • Samples with no predictions: 0 (0.0%)

Coordinate Ascent Strategy:
   • Always predicts exactly one class (single-label consistent)
   • Uses margin rule: argmax(probability - threshold)

📊 Strategy Agreement:
   • Samples where strategies agree: 600 (100.0%)
   • Samples where strategies differ: 0 (0.0%)

📊 Visualize threshold effects

import matplotlib.pyplot as plt

# Plot probability distributions and thresholds
fig, axes = plt.subplots(1, 3, figsize=(15, 5))

for i, (ax, class_name) in enumerate(zip(axes, class_names)):
    # Plot probability distribution for this class
    class_probs = y_prob[:, i]

    # Separate by true class
    true_class_probs = class_probs[y_test == i]
    other_class_probs = class_probs[y_test != i]

    ax.hist(other_class_probs, bins=30, alpha=0.6, label=f'Other classes', color='lightcoral')
    ax.hist(true_class_probs, bins=30, alpha=0.8, label=f'True {class_name}', color='lightblue')

    # Add threshold lines
    ax.axvline(ovr_result.thresholds[i], color='red', linestyle='--',
              label=f'OvR Threshold ({ovr_result.thresholds[i]:.3f})')
    ax.axvline(coord_result.thresholds[i], color='green', linestyle='--',
              label=f'Coord Threshold ({coord_result.thresholds[i]:.3f})')

    ax.set_xlabel(f'Probability for {class_name}')
    ax.set_ylabel('Count')
    ax.set_title(f'Class {i}: {class_name}')
    ax.legend()
    ax.grid(True, alpha=0.3)

plt.tight_layout()
plt.show()

print("📊 The histograms show how optimal thresholds separate true class from others")

📊 The histograms show how optimal thresholds separate true class from others

🚀 What’s Next?

• 04_interactive_demo.ipynb: Deep dive into mathematical foundations

• API Documentation: Explore more advanced multiclass options

💡 Multiclass Strategy Guide

When to use One-vs-Rest (OvR) Independent:

• Multi-label problems: Where samples can belong to multiple classes

• Imbalanced classes: Each class optimized independently

• Different costs per class: Each class can have different error costs

When to use Coordinate Ascent:

• Single-label problems: Where each sample belongs to exactly one class

• Coupled optimization: When class decisions should be consistent

• Margin-based decisions: When you want argmax-style behavior with thresholds

🎯 Advanced Tips

1. Try both strategies: Performance depends on your specific data

2. Cross-validation: Use CV to validate threshold choices

3. Micro vs Macro: Choose averaging based on your problem priorities

4. Class imbalance: OvR often works better for highly imbalanced datasets

5. Computational cost: Coordinate ascent is more expensive but can give better coupled optimization