Machine Learning--Classifying with probability theory: Naive Bayes

Classifying with Bayesian decision

Choose the class with the higher probility, which is the Bayesian decision theory in a nutshell.

Classifying with Conditional Probability

$$p(c_i|[x,j])=\frac{p([x,y]|c_i)p(c_i)}{p([x,y])}$$

Naive Bayes Assumption

1. Independence among all the features.
2. Every feature is equally important.

some Code

Underflow

We can solve the underflow problem by using the the logarithm of probability in our calculations.