统计学习方法

朴素贝叶斯

$$\begin{aligned} P (Y \mid X) &= \frac{P (X \mid Y)P (Y)}{P (X)}\\ &= \frac{P (X \mid Y)P (Y)}{\sum_{i=1}^{ \N} P (X \mid Y_{i})P (Y_{i})} \\ &= \frac{ \prod_{j=1}^{ \mathbb{D}}P (x_{j} \mid Y) P (Y)}{\sum_{i=1}^{ \N} P (X \mid Y_{i})P (Y_{i})} \\ \end{aligned}$$