Q. (Naive Bayes) From Project Gutenberg, we downloaded two files: The Adventures of Sherlock Holmes by Arthur Conan Doyle (pg1661.txt) and The Complete Works of Jane Austen(pg31100.txt). Please develop a multinomial Naive Bayes Classifier that will learn to classify the authors from a snippet of text into: Conan Doyle or Jane Austen. A multinomial Naive Bayes uses a feature vector x = {x 1 , ..., x D } as a histogram and model the posterior probability as:

p(C_k |x) p(C_k ) (i=1 to D) p(x_i |C_k )

where p(x_i |C_k ) can be estimated by the number of times word i was observed in class C_k plus a smoothing factor divided by the total number of words in C_k In the testing phase, given a new example x_t , you can output the class assignment for this example by comparing log p(C₂ |x_t ) and log p(C₂ |x_t ). If log p(C₂ |x_t ) > log p(C₁ |x_t ), assign C 2 to this example. You need to divide the data into training and testing. Make sure the testing data has equal number of samples from Conan Doyle and Jane Austen. Report accuracy on test data using your Naive Bayes classifier. Please do not use any package/tool.