m The following is a typical minimization problem that appears in logistic regression for the classification of two classes of data. The goal is to determine which one of two classes a given data set belongs to. For example, the data set can be a X-ray image of a tumor and the goal is to determine whether the tumor is benign or malignant. The objective function is given by f(w, 8) = $(||||? + B2) + In [1 + exp(-y;(w"; + B)] 12+ j=1 where ) is a regularization parameter, y; = 1 (Class 1) or -1 (Class 2), I; ER" is a vector representing a set of data. The inclusion of the regularization term 1 $(1|0||+ B2) B guarantees that f(w,B) is a strictly convex function. The idea is to use m sets of data to determine/train the weight w eR" and the bias B ER by solving min f(w,B) WER" BER Suppose we have found w and B. Given any new data set I, we can make a decision based on Class 1 if w":+B > 0 I belongs to Class 2 if w": +8 0 I belongs to Class 2 if w": +8