Naïve Bayes Explained with Course Ratings Prediction Example in Python

Naïve Bayes Explained with Course Ratings Prediction Example in Python

Naïve Bayes Explained with Course Ratings Prediction Example in Python

Introduction to Naïve Bayes

Bayes’ Theorem

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Bayes’ Theorem is a mathematical formula that allows us to calculate the ‘reversed’ conditional probabilities. It is often used when we have some prior belief about the probability of an event happening, and want to incorporate that information to calculate the conditional probability of an outcome. We could define the terms as follows:

  • P(A|B) is referred to as the posterior probability
  • P(A) is the prior probability
  • P(B|A) is the likelihood
  • P(B) is the evidence.
  • We can then restate the formula as :

Posterior = Likelihood * Prior / Evidence

Naïve Bayes

  • Given a set of data {(x1,y1) …… (xn,yn)}
  • y takes a limited set of discrete values( categories) from 1 to k

Naïve Bayes applies the concept of Bayes Theorem to compute P(yi=1|xi), P(yi=2|xi) …. P(yi=k|xi) *from the value of *P(xi|yi=1), P(xi|yi=2)….P(xi|yi=k) and the value of P(x) & P(y=1)….P(y=k)

Our prediction is simply the y value that gives the maximum among all P(yi=1|xi), P(yi=2|xi) …. P(yi=k|xi).

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