Problem $9$

a$)$Use a naive Bayes model to determine whether the test case in this table belongs to the "spam" or "not spam" class. Instances $($Doc$)1$ to $4$ are for training the model; instance $5$ is for testing.

b$)$In a real world setting, it is favorable to avoid finding the probability of a test case belonging to a class to be zero. What do you think the reason could be$?$

One method to handle this problem is called Laplace smoothing. Apply this method to the calculations you did in part a$).$

$\backslash$table$[[$training$,$Doc,Words,Class$],[,1,$Money,money,friend,spam$],[,2,$Money,money,bank,spam$],[,3,$Money,hello,spam$],[$test$,4,$Lunch,Lol,money,Not spam$],[,5,$Money,money,money,lunch,Lol,$]]$

Acknowledgements. This document was made by Saman Saffari, Arezoo Haratian, and Pouria Ramazi.