Naive Bayesian method

Naive Bayesian method is a classification method based on Bayesian theorem and independent hypothesis of characteristic condition. , for a given training data set, the joint probability distribution of input and output is studied firstly based on the hypothesis of characteristic condition, and then based on this model, the output Y with the greatest posterior probability is obtained by using Bayesian theorem, and the simple Bayesian method is very efficient for learning and predicting, which is a common method.

The following is mainly about the naïve Bayesian learning methods and classification.

Basic methods:

Set the input space x is contained in the RN is a set of n-dimensional vectors, the output space for the class tag set y={c1,c2,... ck}, the input space for the eigenvector x is x, the output is the class Mark y belongs to y. X is a random vector defined on the input space x , y is a random variable defined on the output space y , and P (x, y) is the joint probability distribution of x, Y, and the training data set is:

t={(X1,y1), (x2,y2),... (Xn,yn)}

Naive Bayesian method learns the joint probability distribution P (x, y) by training data sets. In particular, the following prior probability distributions and conditional probability distributions are studied, prior probability distributions:

P (Y=ck), k=1,2,... K.

Conditional probability distribution:

P (x=x| Y=CK) =p (x (1) =x (1), X (2) =x (2),... X (n) =x (n) | Y=CK), k=1,2,... K.

So we learn the joint probability distribution P (x, y), and the naive Bayes method makes the characteristic condition independent hypothesis for the conditional probability distribution, because of this strong hypothesis, make

P (x=x| Y=CK) =p (x (1) =x (1), X (2) =x (2),... X (n) =x (n) | Y=CK) = multiplicative (j=1-j=n) P (X (j) =x (j) | Y=CK), this hypothesis makes the naive Bayes method a lot simpler.

Naive Bayesian method