Case Study: Naive Bayes Iris

This case study demonstrates Gaussian Naive Bayes classification on the Iris dataset, achieving perfect 100% test accuracy and outperforming k-Nearest Neighbors.

Running the Example

cargo run --example naive_bayes_iris

Results Summary

Test Accuracy: 100% (10/10 correct predictions)

Comparison with kNN

Winner: Naive Bayes (10% accuracy improvement, faster prediction)

Probabilistic Predictions

Sample  Predicted  Setosa  Versicolor  Virginica
──────────────────────────────────────────────────────
   0     Setosa       100.0%    0.0%       0.0%
   1     Setosa       100.0%    0.0%       0.0%
   2     Setosa       100.0%    0.0%       0.0%
   3     Versicolor   0.0%    100.0%       0.0%
   4     Versicolor   0.0%    100.0%       0.0%

Perfect confidence for all predictions - indicates well-separated classes.

Per-Class Performance

All three species classified perfectly.

Variance Smoothing Effect

Robust: Accuracy stable across wide range of smoothing parameters.

Why Naive Bayes Excels Here

1. Well-separated classes: Iris species have distinct feature distributions
2. Gaussian features: Flower measurements approximately normal
3. Small dataset: Only 20 training samples - NB handles small data well
4. Feature independence: Violation of independence assumption doesn't hurt
5. Probabilistic: Full confidence scores for interpretability

Implementation

use aprender::classification::GaussianNB;
use aprender::primitives::Matrix;

// Load data
let (x_train, y_train, x_test, y_test) = load_iris_data()?;

// Train
let mut nb = GaussianNB::new();
nb.fit(&x_train, &y_train)?;

// Predict
let predictions = nb.predict(&x_test)?;
let probabilities = nb.predict_proba(&x_test)?;

// Evaluate
let accuracy = compute_accuracy(&predictions, &y_test);
println!("Accuracy: {:.1}%", accuracy * 100.0);

Key Insights

Advantages Demonstrated

✓ Instant training (<1ms for 20 samples)
✓ 100% accuracy on test set
✓ Perfect confidence scores
✓ Outperforms kNN by 10%
✓ Simple implementation (~240 lines)

When Naive Bayes Wins

• Small datasets (<1000 samples)
• Well-separated classes
• Features approximately Gaussian
• Need probabilistic predictions
• Real-time prediction requirements

When to Use kNN Instead

• Non-linear decision boundaries
• Local patterns important
• Don't assume Gaussian distribution
• Have abundant training data

Related Examples

• examples/knn_iris.rs - kNN comparison
• book/src/ml-fundamentals/naive-bayes.md - Theory