2 Stat 154/254: Statistical Machine Learning Due Sunday October 5th (9pm) 1 Risk minimizers for general zero-one loss Take , and consider the general misclassification loss for postive . In terms of these constants and , find a formula for the optimal classifier, . 2 ROC curves of bad classifiers (a) Let be drawn independently of . Plot the ROC curve for the family of classifiers indexed by . (b) Suppose you have two not-so-great classifiers, A and B, with the following ROC curves. How can you combine them to get a better one? (c) Suppose you have the a terrible classifier with the following ROC curve. How can you use it to make a really good classifier? 3 The behavior of logistic regression with a separating hyperplane Consider logistic loss with regressors and binary responses . Suppose that the data is separable, meaning there exists a such that the data is perfectly classifie