Machine Learning

Chapter 4

Naïve Bayesian Classification

4.1 Introduction

Naïve Bayesian classifiers [1] are simple probabilistic classifiers with their foundation on application of Bayes’ theorem with the assumption of strong (naïve) independence among the features. The following equation [2] states Bayes’ theorem in mathematical terms:

P(A|B)=P(A)P(B|A)P(B)

where:

A and B are events

P(A) and P(B) are the prior probabilities of A and B without regard to each other

P(A|B), also called posterior probability, is the probability of observing event A given that B is true

P(B|A), also called likelihood, is the probability of observing event B given that A is true

Suppose that vector X = (x₁, x₂, … x_n) is an instance (with n independent features) to be classified ...