2. In this question, we will work towards calculating the expected benefit for the SVM model based on the prediction results shown in Table 1, using the expected value framework for the purposes of this question, the recurrence-events class label is considered to be the positive class. We will assume the following benefit matrix, determining the benefit from the perspective of the hospital for each outcome:

(a) Count the number of true positives, true negatives, and false negatives for the SVM model.

Note, as an example to illustrate the process, we can obtain from the table that there are 3 false positives, where the SVM predicted recurrence-events but the actual class label was no-recurrence events instances 5, 9, and 18).

(b) Hence, write down the confusion matrix (a 2 x 2 table containing these same numbers).

(c) Calculate the probability p(h, a) of each entry in the cost matrix, as required for the expected value framework. (Recall that the formula for estimating these probabilities is p(h, a) = count(h, a)/T, where the counts for prediction h and actual class a are obtained from the confusion matrix and T is equal to the number of data points.)

(d) Hence, calculate the expected benefit for our SVM classifier. (Recall that the formula for the expected benefit is p(Y,p) x b(Y,p) + P(N,p) x b(N,p) + P(N, n) b(N, n) + p(Y,n) x b(Y,n).)