Chapter 13 Quiz: Naive Bayes

Chapter 6: Probabilistic Classification — Naive Bayes

Learning objectives

Test your understanding of Bayes theorem, Naive Bayes classifiers, and the independence assumption

This quiz covers both the lecture material and lab exercises from Chapter 13.

Bayes Theorem: $P(C|X) = \frac{P(X|C) \cdot P(C)}{P(X)}$ . Posterior = Likelihood x Prior / Evidence.
Naive Assumption: Features are conditionally independent given the class: $P(X|C) = \prod P(x_i|C)$ .
Variants: Gaussian (continuous), Multinomial (counts/text), Bernoulli (binary).
Laplace Smoothing: $P(x_i|y) = \frac{N_{yi} + \alpha}{N_y + \alpha n}$ prevents zero probabilities.
Strengths: Fast, works with small data. Weakness: Cannot model feature interactions.

Hastie, T., Tibshirani, R., Friedman, J. (2009). The Elements of Statistical Learning (2nd ed.), ch. 6.6. Springer.
Murphy, K.P. (2022). Probabilistic Machine Learning: An Introduction, ch. 9. MIT Press.
James, G., Witten, D., Hastie, T., Tibshirani, R. (2021). An Introduction to Statistical Learning (2nd ed.), ch. 4.4. Springer.