Normalization rescales quantities by their sum so they add to one while preserving their relative ratio. It turns competing probability weights into a valid probability distribution. section 8.2
Filtering spam probabilities
After restricting attention to emails containing “lottery,” only spam and ham remain possible. Divide each corresponding probability by their sum; the normalized results are 3/4 and 1/4, which add to one. section 8.2
Apply normalization in three steps:
- Identify the possible cases that remain after conditioning on the observed event. section 8.2
- Add their unnormalized quantities to obtain the total. section 8.2
- Divide every quantity by that total. section 8.2
Figure 8.9 From the tree in figure 8.8, we have removed the two branches where the emails don’t contain the word lottery.
The reduced probability tree makes normalization intuitive: remove impossible branches, then redistribute the remaining relative weights so they sum to one. section 8.2
