Introduction #
$$ P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)} $$
Translating this matematical formula to words:
What is the probability that some event A happening, given that B happened?
We call B condition
Expand Naive Bayes #
$$ \text{posterior} = \frac{\text{likelihood} \cdot \text{prior}}{\text{evidence}} $$ $$ P(C_k | x) = \frac{P(x | C_k) \cdot P(C_k)}{P(x)} $$ C_k: category x: feature vector
$$ P(C_k | x_1, x_2, \dots, x_n) \propto P(C_k) \prod_{i=1}^{n} P(x_i | C_k) $$ We are assuming that each x is independent