This question examines some modifications on the loss function min$-$

imization framework introduced in class, in the setting of binary classification. Specifically, we

assume that the features are collected in a vector x in Rp$,$ the dependent variable is binary

y in $\{1,+1\},$ and our goal is to learn a function f : Rp $->$ R$.$ In order to use f to make

predictions, we adopt the prediction rule