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5. Linear/Logistic Regression [10 points] (a) [5 points] In lecture, we considered using linear regression for binary classification on the targets {0, 1}. Here, we use a linear model y = wxtb and squared error loss C(y, t) = }(y -t)'. We saw this has the problem that it penalizes confident correct predictions. Will it fix this problem if we instead use a modified hinge loss, shown below? t = 0, [ly, t ) = it = 1, max(0, y) 1 - min(1, y) Justify your answer mathematically. (b) [5 points] Consider the logistic regression model y = g(w x), trained using the binary cross entropy loss function, where g(2) = 1 is the sigmoid function. Your friend proposes a modified version of logistic regression, using g(2) = Ite The model would still be trained using the binary cross entropy loss. How would the learnt model parameters, as well as the model predictions, differ from conven- tional logistic regression? Justify your answer mathematically. A purely graphical explanation is not sufficient