Exercise 8.7 Regularizing separate terms in 2d logistic regression (Source: Jaaakkola.) a. Consider the data in Figure 8.13, where we fit the model p(y = lk,w) (uo + w1z1 + w2z2). Suppose we fit the model by maximum likelihood, i.e., we minimize J(w) =-1(w, Dtrain) (8.133) where [(w, Dtrain) is the log likelihood on the training set. Sketch a possible decision boundary corresponding to w. (Copy the figure first (a rough sketch is enough), and then superimpose your answer on your copy, since you will need multiple versions of this figure) Is your answer (decision boundary) unique? How many classification errors does your method make on the training set? b. Now suppose we regularize only the wo parameter, i.e., we minimize (8.134) Suppose is a very large number, so we regularize wo all the way to 0, but all other parameters are unregularized. make on the training set? Hint: consider the behavior of simple linear regression, ww2 when 10. Sketch a possible decision boundary. How many classification errors does your n ethod c. Now suppose we heavily regularize only the w1 parameter, i.e., we minimize (8.135) Sketch a possible decision boundary. How many classification errors does your method make on the training set? 8.6. Generative vs discriminative classifiers 279 X2 0 o Figure 8.13 Data for logistic regression question. d. Now suppose we heavily regularize only the w2 parameter. Sketch a possible decision boundary. How s your method make on the training set? y classification errors doe man