# Naive Bayes Classifier

Could someone please explain to me how and why can we go from equation $$4.3$$ to equation $$4.4$$:

$$\hat{c}= \arg\max_{c \in \mathcal{C}}P(c|d) = \arg\max_{c \in \mathcal{C}}\frac{P(d|c)P(c)}{P(d)}\tag{4.3}$$

$$\hat{c}= \arg\max_{c \in \mathcal{C}}P(c|d) = \arg\max_{c \in \mathcal{C}}P(d|c)P(c)\tag{4.4}$$

## 2 Answers

We are trying to select the optimal $$c$$, here $$d$$ is fixed and hence $$P(d)$$ and $$\frac1{P(d)}$$ is just a positive constant.

Multiplying an objective function with a positive constant doesn't change the optimal solution, hence we can drop $$P(d)$$.

Because P(d) is constant in terms of c, so it doesn't affect the location of the maximum (only its size but we don't care about that).