Types of Classification Algorithms : Part - 2 Naïve Bayes classifier

Helloooo Friends!!!

In the previous article, we have seen Bayes' theorem now we are going to learn Naive Bayes' classifiers.

• It is based on Bayes' theorem.
• It gives a strong predicted answer by applying Bayes' theorem. So, it is known as Naive Bayes' classifier.

Now, let's start with How does it work?

Let's take an example if we want to approve an application for a credit card, we need to check the age of a person, an income of a person, credit score, year of employment of a person, debts of a person, etc. Now we have two possibilities, approved or not approved. So, if we consider our outcomes as Res=1 if approved and Res=0 if not approved.

Add this problem to Bayes' equation so our problem with formula becomes something like:

Fig. 1 Whether to approve the application of credit card or not using Bayes' Theorem

Now we get the result Res=1 if the P(Res = 1 | x1,....,xn) > P(Res = 0 | x1,....,xn) otherwise Res=0.
P(Res = 1) is the prior probability, it works without knowing the values of x. (Here, x = {x1,x2,..., xn}).  So, that it works for P(Res = 0) + P(Res = 1) = 1. As we all know the total probability is 1. 
Next thing that we can to consider, P(Res | x1,....,xn) is class likelihood is the conditional probability that is Res has associated value of x.

And lastly, we have evidence or marginal probability is P(x1,....,xn) and is work when we consider the value of x, and we do not think whether the value of x is positive or negative.

Afterward, we can get the posterior probability is the combination of prior and result of Bayes' rule. So, as we have already discussed about that but again we think in the formula for our example with posterior probability is something like

Fig. 2 Posterior Probability

And Bayes' classifier chooses the result with the highest posterior probability from all the result. See the below formula for Bayes' classifier.

Fig. 3 Bayes' Classifier

So, in a simple meaning of Bayes' classifier, it is based on conditional probability and Bayes' rule, check for the posterior probability and choose the maximum or highest posterior probability to achieve the Classification task.

Now it is simple, isn't it? I hope you enjoy and learn this classifier easily.