Programming question: Naive Bayes Classi er to De- tect Credit Card Fraud. In this question you are asked to t Naive Bayes Classi er to detect credit card fraud using de-identi ed credit card transactions labeled as fraudulent or genuine. The below description was adopted from kaggle website. The datasets contains transactions made by credit cards in September 2013 by Eu- ropean cardholders. This dataset presents transactions that occurred in two days, where we have 492 frauds out of 284,807 transactions. The dataset is highly unbalanced, the positive class (frauds) account for 0.172% of all transactions. It contains only numerical input variables which are the result of a PCA transfor- mation. Unfortunately, due to con dentiality issues, we cannot provide the original features and more background information about the data. Features V1, V2, ... V28 are the principal components obtained with PCA, the only features which have not been transformed with PCA are 'Time' and 'Amount'. Feature 'Time' contains the seconds elapsed between each transaction and the rst transaction in the dataset. The feature 'Amount' is the transaction Amount, this feature can be used for example-dependant cost-senstive learning. Feature 'Class' is the response variable and it takes value 1 in case of fraud and 0 otherwise. Please treat V1 to V28 as continuous features and use Gaussian distribution for training as I demonstrated in the lecture, i.e., P(V1 mid Class) is Gaussian, to calcula- tion the class-conditional probabilities in training. And treat `Time' and `Amount' as discrete features by discretizing them into 2 states for the former and 3 states for the latter, for example, Low/Medium/High and Near/Far. You should divide the data into a training set (80%) and a test set (20%) and calculate precision, recall and F-score. Data can be downloaded from: https://www.kaggle.com/dalpozz/creditcardfraud/data