[Statistical Learning｜Book Reading] Chapter 4 Naive Bayes p47-p54

train of thought

Naive Bayesian method is a classification method based on Bayesian theorem and the independent assumption of feature conditions. For a given training data set, firstly learn the joint probability distribution of input/output based on the independent assumptions of the characteristic feature conditions; then based on this model, for a given input, use Bayes theorem to find the output y with the largest posterior probability.

Naive Bayesian Learning and Classification

Naive Bayesian learning strategy:
$$y=f(x)=arg\underset{c_k}{\max }P(Y)=c_k)\prod _{j}P(X^{(j)}=x^{(j)}|Y=c_k)$$

Posterior probability maximization:
$$f\left(x\right)=arg\underset{c_k}{\max }P(c_k｜X=x)$$

Parameter Estimation Algorithm of Naive Bayes Method

maximum likelihood estimation

Bayesian estimation