5. (20 points) In Support Vector Machines, the following equations can be observed. - wx++b=+1 - wx+b=1 x+=w+x - x+x=M (a) (12 points) Show that "maximizing the margin M " becomes an optimization problem that minimizes ww. (b) (8 points) We viewed the SVM optimization problem from two perspectives and formed a Lagrangian Dual problem. What are the two problems; describe them in your own language. 4. (15 points) Using the dataset below, we want to build a decision tree which classifies whether the given URL is phishing or not. Calculate the conditional entropy of all the attributes and find the best attribute for the first branch of the decision tree. Note, you can assume the entropy of the zero probability to be 0 , since limp0plogp= 0. 5. (20 points) In Support Vector Machines, the following equations can be observed. - wx++b=+1 - wx+b=1 x+=w+x - x+x=M (a) (12 points) Show that "maximizing the margin M " becomes an optimization problem that minimizes ww. (b) (8 points) We viewed the SVM optimization problem from two perspectives and formed a Lagrangian Dual problem. What are the two problems; describe them in your own language. 4. (15 points) Using the dataset below, we want to build a decision tree which classifies whether the given URL is phishing or not. Calculate the conditional entropy of all the attributes and find the best attribute for the first branch of the decision tree. Note, you can assume the entropy of the zero probability to be 0 , since limp0plogp= 0