Suppose we have a binary (0-1) classification problem with the following training data points: r4 (2,3); 41 where xi's are the feature vectors, and the y's are the labels. Hence, for this particular training dataset the points 1 and x4 belong to one class, and the points x2, r3 belong to a different class. Our goal is to learn a model that, given a data point r, correctly identi- fies if x belongs to the class y = 1 or y = 0. (a) Model this classification problem as a logistic regression problem and form the max likelihood logistic regression program for this problem (b) Write the KKT conditions for the logistic regression problem (c) Solve the optimization problem, you can use a solver. What are the values of the decision variables A-, and what are the probabilities for each training data point according to the model? (d) Model this same classification problem as a support vector machine, using the regularized min violation formulation that we introduced in lecture, with penalty = 1. (e) Write the KKT conditions for the SVM. Suppose we have a binary (0-1) classification problem with the following training data points: r4 (2,3); 41 where xi's are the feature vectors, and the y's are the labels. Hence, for this particular training dataset the points 1 and x4 belong to one class, and the points x2, r3 belong to a different class. Our goal is to learn a model that, given a data point r, correctly identi- fies if x belongs to the class y = 1 or y = 0. (a) Model this classification problem as a logistic regression problem and form the max likelihood logistic regression program for this problem (b) Write the KKT conditions for the logistic regression problem (c) Solve the optimization problem, you can use a solver. What are the values of the decision variables A-, and what are the probabilities for each training data point according to the model? (d) Model this same classification problem as a support vector machine, using the regularized min violation formulation that we introduced in lecture, with penalty = 1. (e) Write the KKT conditions for the SVM