Problem 1. (20 points) Naive Bayes classifier. Consider a binary classification problem where there are eight data points in the training set. That is, D = {(-1, -1, -1, -), (-1, -1, 1, +), (-1, 1, -1, +), (-1, 1, 1, -), (1,-1, -1, +), (1, -1,1, -), (1,1,-1, -), (1, 1, 1, +) }, where each tuple (X1, X2, 23, y) represents a training example with input vector (X1, X2, 23) and class label y. a) (10 points) Construct a naive Bayes classifier for this problem and evaluate its accuracy on the training set. Measure accuracy as the fraction of correctly classified examples. b) (10 points) Transform the input space into a higher-dimensional space (1, X1, X2, X3, X1X2, X1X3, X23, 21, 12, 23, 2412, 2122, X13, 1213, 1243, 21, 12, 23, 21X23) and repeat the previous step. Carry out all steps manually and show all your calculations