(b) Find a linear classifier that makes at most one error on the training data . The classifier should be of the form, 1: = 1 if 2 ; > 0 if z ; 0 is a positive scalar. Would using the new parameters change the values y in part (b)? Would they change the likelihoods P(y;|x; ) in part (c)? If they do not change state why. If they do change, qualitatively describe the change as a function of a. 4. Suppose we collect data for a group of students in a machine learning class with variables X1 = hours studied , X2 = undergrad GPA, and Y = receive an A. We fit a logistic regression and produce estimated coefficient 8 , = -6,8 1 = 0.05, B 2 = 1. (a) Estimate the probability that a student who studies for 40 h and has an undergrad GPA of 3.5 gets an A in the class . (b) How many hours would the student in part (a) need to study to have a 50 % chance of getting an A in the class ? 5. The loss function for logistic regression for binary classification is the binary cross entropy defined as J ( 3 ) = [ In (1 + e = ) - yiz: where zi =B o +3 101i +8 242; for two features 1 1,; and T2,i. (a) What are the partial derivatives of z; with respect to of 1, and B 2. (b) Compute the partial derivatives of J(B) with respect to8 0 8 1, and B 2. You should use the chain rule of differentiation. (c) Can you find the close form expressions for the optimal parameters 8 0,8 1, and B 2 by putting the derivatives of J(B) to 0? What methods can be used to optimize the loss function J(B)