Naive Bayes Algorithm

Naive Bayes Classifier is based on Bayes theorem which gives the conditional probabity of an event A given B

Recap from conditional probability - given random variables X and Y, probability of X given Y can be expressed as:
     P(X | Y) = P(X∩Y) / P(Y)
The same can be written for Y given X as:
     P(Y | X) = P(Y∩X) / P(X)
Since P(X∩Y) = P(Y∩X), solving both equations gives:
     P(X∩Y) = P(X | Y) P(Y) = P(Y | X) P(X)
We can rewrite conditional probability of X given Y as:
     P(X | Y) = P(Y | X) P(X) / P(Y)
This is known as Bayes theorem. In plain English, this can be written as
Naive Bayes algorithm

Where is Naive Bayes used

Some of real world examples are as given below
  • To mark an email as spam, or not spam
  • Categorize a news article about technology, politics, or sports
  • Check a piece of text expressing positive emotions, or negative emotions
  • Medical Diagnosis- human body is in high risk or nor risk with cancer.
  • Face recognition softwares to identify nose, mouth, eyes

Probability of Tossing two coins

Channces of outcome when toss two coins:{HH, HT, TH, TT}
P(Getting two heads) = 1/4
P(Atleast one tails) = 3/4
P(Second coin being head give first coin is tail) = 1/2
P(Getting two heads given first coin is a head) = 1/2
Formual of naive bayes algorithm

Formual of naive bayes algorithm11

This is very simple and we know all the values of each occurrence, To understand bayes thearom will use this problem. Formual of naive bayes algorithm solution