Let's start with understanding the magic behind the algorithm—how Naïve Bayes works. Given a data sample x with n features, x1, x2, …, xn (x represents a feature vector and x = (x1, x2, …, xn)), the goal of Naïve Bayes is to determine the probabilities that this sample belongs to each of K possible classes y1, y2, …, yK, that is P( yk |x) or P(x1, x2, …, xn), where k = 1, 2, …, K. It looks no different from what we have just dealt with: x, or x1, x2, …, xn, is a joint event that the sample has features with values x1, x2, …, xn respectively, yk is an event that the sample belongs to class k. We can apply Bayes' theorem right away:
Let's look at each component in detail:
- P (yk) portrays how classes are distributed, ...
