14.8 Summary

Naive Bayes

\[f(y | x_{1}, x_{2}, ..., x_{p}) = \frac{f(y) \cdot L(y | x_{1}, x_{2}, ..., x_{p})}{\sum_{y'} f(y') \cdot L(y' | x_{1}, x_{2}, ..., x_{p})}\]

• conditionally independent \(\rightarrow\) computationally efficient
• generalizes to more than two categories
• assumptions violated commonly in practice

Logistic Regression

\[\log\left(\frac{\pi}{1-\pi}\right) = \beta_{0} + \beta_{1}X_{1} + \cdots + \beta_{k}X_{p}\]

• binary classification
• coefficients \(\rightarrow\) illumination of the relationships among these variables