Naive Bayes Classifier¶

Sanjiv R. Das

What is Naive Bayes?¶

Classification based on the class with the highest posterior probability:

$$Pr[C_j | x_1,...,x_n] = \frac{Pr[x_1,...,x_n | C_j] \cdot Pr[C_j]}{\sum_i Pr[x_1,...,x_n | C_i] \cdot Pr[C_i]}$$

and

$$Pr[x_1,...,x_n | C_j] = f[x_1|C_j] \cdot f[x_2|C_j] \cdots f[x_n|C_j]$$

where the last equation encapsulates "naivety", i.e., $x_1,...,x_n$ are independent and Gaussian with density function $f(x) \sim N(\mu_x, \sigma_x^2)$, computed from the raw data.